Transcript
Operation Research Techniques
Project Report On
Application of
Operation Research Techniques
Subject Operation Research
Submitted to Prof PM Bhole
Prepared by Mohd Adil (45)
Date 1732011
1
Operation Research Techniques
ACKNOWLEDGEMENT
First and foremost let I sincerely thank ALMIGHTY for the
great opportunity and blessings that he has showered up on
us for the successful and timely completion of our project
work
I extent my sincere gratitude to Dr Vidya Hatangadi
Director of AIAIMS for her kind support and guidance for
making our project great success
I extent my sincere gratitude to guide Mr PM Bhole
lecturer Allana Institute of Management Studies for the
kind support and proper guidance without which the project
would not have been efficiently completed
I render my whole hearted thanks to librarian for their
assistance and co-operation given to me in regard to this
work
Once again I take this opportunity to convey me sincere
thanks to each and every person who helped me directly
and indirectly in the successful completion of this project
2
Operation Research Techniques
CONTENTS
SRNO TOPICS PAGE NO
1 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
04----05
2 Structure of Linear Programminghelliphelliphelliphelliphelliphelliphellip
06----08
3 Assumptions of Linear Programming helliphelliphelliphellip
09----11
4 Limitations of Linear Programminghelliphelliphelliphelliphellip
12----12
5 Applications of Linear Programminghelliphelliphelliphelliphellip
13----15
6 Case Studyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
16----26
7 Conclusionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
27---27
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Operation Research Techniques
8 Bibliographyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
28---28
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INTRODUCTIONIn a decision-making embroilment model formulation is important
because it represents the essence of business decision problem The
term formulation is used to mean the process of converting the
verbal description and numerical data into mathematical expressions
which represents the relevant relationship among decision factors
objectives and restrictions on the use of resources Linear
Programming (LP) is a particular type of technique used for economic
allocation of scarce or limited resources such as labour material
machine time warehouse space capital energy etc to several
competing activities such as products services jobs new equipment
projects etc on the basis of a given criterion of optimally The phrase
scarce resources mean resources that are not in unlimited in
availability during the planning period The criterion of optimality
generally is either performance return on investment profit cost
utilily time distance etc
George B Dantzing while working with US Air Force during World War
II developed this technique primarily for solving military logistics
problems But now it is being used extensively in all functional areas
of management hospitals airlines agriculture military operations oil
refining education energy planning pollution control transportation
planning and scheduling research and development etc Even
though these applications are diverse all IP models consist of certain
common properties and assumptions Before applying linear
programming to a real-life decision problem the decision-maker must
be aware of all these properties and assumptions which are
discussed later in this chapter
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Operation Research Techniques
Before discussing in detail the basic concepts and applications of
linear programming let us be clear about the two words linear and
programming The word linear refers to linear relationship among
variables in a model Thus a given change in one variable will always
cause a resulting proportional change in another variable For
example doubling the investment on a certain project will exactly
double the rate of return The word programming refers to modelling
and solving a problem mathematically that involves the economic
allocation of limited resources by choosing a particular course of
action or strategy among various alternative strategies to achieve
the desired objective
A large number of computer packages are available for solving a
mathematical LP model but there is no general package for building a
model Model building is an art that improves with practice To
illustrate how to build IP models a variety of examples are given in
this chapter
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Operation Research Techniques
STRUCTURE OF LINEAR PROGRAMMING
General Structure of LP Model
The general structure of LP model consists of three components
Decision variables (activities)
We need to evaluate various alternatives (courses of action) for
arriving at the optimal value of objective function Obviously if there
are no alternatives to select from we would not need LP The
evaluation of various alternatives is guided by the nature of objective
function and availability of resources For this we pursue certain
activities usually denoted by x1 x2hellipxn The value of these activities
represents the extent to which each of these is performed For
example in a product-mix manufacturing the management may use
LP to decide how many units of each of the product to manufacture
by using its limited resources such as personnel machinery money
material etc
These activities are also known as decision variables because they
arc under the decision-makers control These decision variables
usually interrelated in terms of consumption of limited resources
require simultaneous solutions All decision variables are
continuous controllable and non-negative That is x1gt0
x2gt0 xngt0
The objective function
The objective function of each LP problem is a mathematical
representation of the objective in terms of a measurable quantity
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such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
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Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
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Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
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Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
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Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
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Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
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Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
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Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
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Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
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Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
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Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
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Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
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Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
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Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
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Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
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Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
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Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
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Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
ACKNOWLEDGEMENT
First and foremost let I sincerely thank ALMIGHTY for the
great opportunity and blessings that he has showered up on
us for the successful and timely completion of our project
work
I extent my sincere gratitude to Dr Vidya Hatangadi
Director of AIAIMS for her kind support and guidance for
making our project great success
I extent my sincere gratitude to guide Mr PM Bhole
lecturer Allana Institute of Management Studies for the
kind support and proper guidance without which the project
would not have been efficiently completed
I render my whole hearted thanks to librarian for their
assistance and co-operation given to me in regard to this
work
Once again I take this opportunity to convey me sincere
thanks to each and every person who helped me directly
and indirectly in the successful completion of this project
2
Operation Research Techniques
CONTENTS
SRNO TOPICS PAGE NO
1 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
04----05
2 Structure of Linear Programminghelliphelliphelliphelliphelliphelliphellip
06----08
3 Assumptions of Linear Programming helliphelliphelliphellip
09----11
4 Limitations of Linear Programminghelliphelliphelliphelliphellip
12----12
5 Applications of Linear Programminghelliphelliphelliphelliphellip
13----15
6 Case Studyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
16----26
7 Conclusionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
27---27
3
Operation Research Techniques
8 Bibliographyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
28---28
4
Operation Research Techniques
INTRODUCTIONIn a decision-making embroilment model formulation is important
because it represents the essence of business decision problem The
term formulation is used to mean the process of converting the
verbal description and numerical data into mathematical expressions
which represents the relevant relationship among decision factors
objectives and restrictions on the use of resources Linear
Programming (LP) is a particular type of technique used for economic
allocation of scarce or limited resources such as labour material
machine time warehouse space capital energy etc to several
competing activities such as products services jobs new equipment
projects etc on the basis of a given criterion of optimally The phrase
scarce resources mean resources that are not in unlimited in
availability during the planning period The criterion of optimality
generally is either performance return on investment profit cost
utilily time distance etc
George B Dantzing while working with US Air Force during World War
II developed this technique primarily for solving military logistics
problems But now it is being used extensively in all functional areas
of management hospitals airlines agriculture military operations oil
refining education energy planning pollution control transportation
planning and scheduling research and development etc Even
though these applications are diverse all IP models consist of certain
common properties and assumptions Before applying linear
programming to a real-life decision problem the decision-maker must
be aware of all these properties and assumptions which are
discussed later in this chapter
5
Operation Research Techniques
Before discussing in detail the basic concepts and applications of
linear programming let us be clear about the two words linear and
programming The word linear refers to linear relationship among
variables in a model Thus a given change in one variable will always
cause a resulting proportional change in another variable For
example doubling the investment on a certain project will exactly
double the rate of return The word programming refers to modelling
and solving a problem mathematically that involves the economic
allocation of limited resources by choosing a particular course of
action or strategy among various alternative strategies to achieve
the desired objective
A large number of computer packages are available for solving a
mathematical LP model but there is no general package for building a
model Model building is an art that improves with practice To
illustrate how to build IP models a variety of examples are given in
this chapter
6
Operation Research Techniques
STRUCTURE OF LINEAR PROGRAMMING
General Structure of LP Model
The general structure of LP model consists of three components
Decision variables (activities)
We need to evaluate various alternatives (courses of action) for
arriving at the optimal value of objective function Obviously if there
are no alternatives to select from we would not need LP The
evaluation of various alternatives is guided by the nature of objective
function and availability of resources For this we pursue certain
activities usually denoted by x1 x2hellipxn The value of these activities
represents the extent to which each of these is performed For
example in a product-mix manufacturing the management may use
LP to decide how many units of each of the product to manufacture
by using its limited resources such as personnel machinery money
material etc
These activities are also known as decision variables because they
arc under the decision-makers control These decision variables
usually interrelated in terms of consumption of limited resources
require simultaneous solutions All decision variables are
continuous controllable and non-negative That is x1gt0
x2gt0 xngt0
The objective function
The objective function of each LP problem is a mathematical
representation of the objective in terms of a measurable quantity
7
Operation Research Techniques
such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
8
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
CONTENTS
SRNO TOPICS PAGE NO
1 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
04----05
2 Structure of Linear Programminghelliphelliphelliphelliphelliphelliphellip
06----08
3 Assumptions of Linear Programming helliphelliphelliphellip
09----11
4 Limitations of Linear Programminghelliphelliphelliphelliphellip
12----12
5 Applications of Linear Programminghelliphelliphelliphelliphellip
13----15
6 Case Studyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
16----26
7 Conclusionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
27---27
3
Operation Research Techniques
8 Bibliographyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
28---28
4
Operation Research Techniques
INTRODUCTIONIn a decision-making embroilment model formulation is important
because it represents the essence of business decision problem The
term formulation is used to mean the process of converting the
verbal description and numerical data into mathematical expressions
which represents the relevant relationship among decision factors
objectives and restrictions on the use of resources Linear
Programming (LP) is a particular type of technique used for economic
allocation of scarce or limited resources such as labour material
machine time warehouse space capital energy etc to several
competing activities such as products services jobs new equipment
projects etc on the basis of a given criterion of optimally The phrase
scarce resources mean resources that are not in unlimited in
availability during the planning period The criterion of optimality
generally is either performance return on investment profit cost
utilily time distance etc
George B Dantzing while working with US Air Force during World War
II developed this technique primarily for solving military logistics
problems But now it is being used extensively in all functional areas
of management hospitals airlines agriculture military operations oil
refining education energy planning pollution control transportation
planning and scheduling research and development etc Even
though these applications are diverse all IP models consist of certain
common properties and assumptions Before applying linear
programming to a real-life decision problem the decision-maker must
be aware of all these properties and assumptions which are
discussed later in this chapter
5
Operation Research Techniques
Before discussing in detail the basic concepts and applications of
linear programming let us be clear about the two words linear and
programming The word linear refers to linear relationship among
variables in a model Thus a given change in one variable will always
cause a resulting proportional change in another variable For
example doubling the investment on a certain project will exactly
double the rate of return The word programming refers to modelling
and solving a problem mathematically that involves the economic
allocation of limited resources by choosing a particular course of
action or strategy among various alternative strategies to achieve
the desired objective
A large number of computer packages are available for solving a
mathematical LP model but there is no general package for building a
model Model building is an art that improves with practice To
illustrate how to build IP models a variety of examples are given in
this chapter
6
Operation Research Techniques
STRUCTURE OF LINEAR PROGRAMMING
General Structure of LP Model
The general structure of LP model consists of three components
Decision variables (activities)
We need to evaluate various alternatives (courses of action) for
arriving at the optimal value of objective function Obviously if there
are no alternatives to select from we would not need LP The
evaluation of various alternatives is guided by the nature of objective
function and availability of resources For this we pursue certain
activities usually denoted by x1 x2hellipxn The value of these activities
represents the extent to which each of these is performed For
example in a product-mix manufacturing the management may use
LP to decide how many units of each of the product to manufacture
by using its limited resources such as personnel machinery money
material etc
These activities are also known as decision variables because they
arc under the decision-makers control These decision variables
usually interrelated in terms of consumption of limited resources
require simultaneous solutions All decision variables are
continuous controllable and non-negative That is x1gt0
x2gt0 xngt0
The objective function
The objective function of each LP problem is a mathematical
representation of the objective in terms of a measurable quantity
7
Operation Research Techniques
such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
8
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
8 Bibliographyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip
28---28
4
Operation Research Techniques
INTRODUCTIONIn a decision-making embroilment model formulation is important
because it represents the essence of business decision problem The
term formulation is used to mean the process of converting the
verbal description and numerical data into mathematical expressions
which represents the relevant relationship among decision factors
objectives and restrictions on the use of resources Linear
Programming (LP) is a particular type of technique used for economic
allocation of scarce or limited resources such as labour material
machine time warehouse space capital energy etc to several
competing activities such as products services jobs new equipment
projects etc on the basis of a given criterion of optimally The phrase
scarce resources mean resources that are not in unlimited in
availability during the planning period The criterion of optimality
generally is either performance return on investment profit cost
utilily time distance etc
George B Dantzing while working with US Air Force during World War
II developed this technique primarily for solving military logistics
problems But now it is being used extensively in all functional areas
of management hospitals airlines agriculture military operations oil
refining education energy planning pollution control transportation
planning and scheduling research and development etc Even
though these applications are diverse all IP models consist of certain
common properties and assumptions Before applying linear
programming to a real-life decision problem the decision-maker must
be aware of all these properties and assumptions which are
discussed later in this chapter
5
Operation Research Techniques
Before discussing in detail the basic concepts and applications of
linear programming let us be clear about the two words linear and
programming The word linear refers to linear relationship among
variables in a model Thus a given change in one variable will always
cause a resulting proportional change in another variable For
example doubling the investment on a certain project will exactly
double the rate of return The word programming refers to modelling
and solving a problem mathematically that involves the economic
allocation of limited resources by choosing a particular course of
action or strategy among various alternative strategies to achieve
the desired objective
A large number of computer packages are available for solving a
mathematical LP model but there is no general package for building a
model Model building is an art that improves with practice To
illustrate how to build IP models a variety of examples are given in
this chapter
6
Operation Research Techniques
STRUCTURE OF LINEAR PROGRAMMING
General Structure of LP Model
The general structure of LP model consists of three components
Decision variables (activities)
We need to evaluate various alternatives (courses of action) for
arriving at the optimal value of objective function Obviously if there
are no alternatives to select from we would not need LP The
evaluation of various alternatives is guided by the nature of objective
function and availability of resources For this we pursue certain
activities usually denoted by x1 x2hellipxn The value of these activities
represents the extent to which each of these is performed For
example in a product-mix manufacturing the management may use
LP to decide how many units of each of the product to manufacture
by using its limited resources such as personnel machinery money
material etc
These activities are also known as decision variables because they
arc under the decision-makers control These decision variables
usually interrelated in terms of consumption of limited resources
require simultaneous solutions All decision variables are
continuous controllable and non-negative That is x1gt0
x2gt0 xngt0
The objective function
The objective function of each LP problem is a mathematical
representation of the objective in terms of a measurable quantity
7
Operation Research Techniques
such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
8
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
INTRODUCTIONIn a decision-making embroilment model formulation is important
because it represents the essence of business decision problem The
term formulation is used to mean the process of converting the
verbal description and numerical data into mathematical expressions
which represents the relevant relationship among decision factors
objectives and restrictions on the use of resources Linear
Programming (LP) is a particular type of technique used for economic
allocation of scarce or limited resources such as labour material
machine time warehouse space capital energy etc to several
competing activities such as products services jobs new equipment
projects etc on the basis of a given criterion of optimally The phrase
scarce resources mean resources that are not in unlimited in
availability during the planning period The criterion of optimality
generally is either performance return on investment profit cost
utilily time distance etc
George B Dantzing while working with US Air Force during World War
II developed this technique primarily for solving military logistics
problems But now it is being used extensively in all functional areas
of management hospitals airlines agriculture military operations oil
refining education energy planning pollution control transportation
planning and scheduling research and development etc Even
though these applications are diverse all IP models consist of certain
common properties and assumptions Before applying linear
programming to a real-life decision problem the decision-maker must
be aware of all these properties and assumptions which are
discussed later in this chapter
5
Operation Research Techniques
Before discussing in detail the basic concepts and applications of
linear programming let us be clear about the two words linear and
programming The word linear refers to linear relationship among
variables in a model Thus a given change in one variable will always
cause a resulting proportional change in another variable For
example doubling the investment on a certain project will exactly
double the rate of return The word programming refers to modelling
and solving a problem mathematically that involves the economic
allocation of limited resources by choosing a particular course of
action or strategy among various alternative strategies to achieve
the desired objective
A large number of computer packages are available for solving a
mathematical LP model but there is no general package for building a
model Model building is an art that improves with practice To
illustrate how to build IP models a variety of examples are given in
this chapter
6
Operation Research Techniques
STRUCTURE OF LINEAR PROGRAMMING
General Structure of LP Model
The general structure of LP model consists of three components
Decision variables (activities)
We need to evaluate various alternatives (courses of action) for
arriving at the optimal value of objective function Obviously if there
are no alternatives to select from we would not need LP The
evaluation of various alternatives is guided by the nature of objective
function and availability of resources For this we pursue certain
activities usually denoted by x1 x2hellipxn The value of these activities
represents the extent to which each of these is performed For
example in a product-mix manufacturing the management may use
LP to decide how many units of each of the product to manufacture
by using its limited resources such as personnel machinery money
material etc
These activities are also known as decision variables because they
arc under the decision-makers control These decision variables
usually interrelated in terms of consumption of limited resources
require simultaneous solutions All decision variables are
continuous controllable and non-negative That is x1gt0
x2gt0 xngt0
The objective function
The objective function of each LP problem is a mathematical
representation of the objective in terms of a measurable quantity
7
Operation Research Techniques
such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
8
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
Before discussing in detail the basic concepts and applications of
linear programming let us be clear about the two words linear and
programming The word linear refers to linear relationship among
variables in a model Thus a given change in one variable will always
cause a resulting proportional change in another variable For
example doubling the investment on a certain project will exactly
double the rate of return The word programming refers to modelling
and solving a problem mathematically that involves the economic
allocation of limited resources by choosing a particular course of
action or strategy among various alternative strategies to achieve
the desired objective
A large number of computer packages are available for solving a
mathematical LP model but there is no general package for building a
model Model building is an art that improves with practice To
illustrate how to build IP models a variety of examples are given in
this chapter
6
Operation Research Techniques
STRUCTURE OF LINEAR PROGRAMMING
General Structure of LP Model
The general structure of LP model consists of three components
Decision variables (activities)
We need to evaluate various alternatives (courses of action) for
arriving at the optimal value of objective function Obviously if there
are no alternatives to select from we would not need LP The
evaluation of various alternatives is guided by the nature of objective
function and availability of resources For this we pursue certain
activities usually denoted by x1 x2hellipxn The value of these activities
represents the extent to which each of these is performed For
example in a product-mix manufacturing the management may use
LP to decide how many units of each of the product to manufacture
by using its limited resources such as personnel machinery money
material etc
These activities are also known as decision variables because they
arc under the decision-makers control These decision variables
usually interrelated in terms of consumption of limited resources
require simultaneous solutions All decision variables are
continuous controllable and non-negative That is x1gt0
x2gt0 xngt0
The objective function
The objective function of each LP problem is a mathematical
representation of the objective in terms of a measurable quantity
7
Operation Research Techniques
such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
8
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
STRUCTURE OF LINEAR PROGRAMMING
General Structure of LP Model
The general structure of LP model consists of three components
Decision variables (activities)
We need to evaluate various alternatives (courses of action) for
arriving at the optimal value of objective function Obviously if there
are no alternatives to select from we would not need LP The
evaluation of various alternatives is guided by the nature of objective
function and availability of resources For this we pursue certain
activities usually denoted by x1 x2hellipxn The value of these activities
represents the extent to which each of these is performed For
example in a product-mix manufacturing the management may use
LP to decide how many units of each of the product to manufacture
by using its limited resources such as personnel machinery money
material etc
These activities are also known as decision variables because they
arc under the decision-makers control These decision variables
usually interrelated in terms of consumption of limited resources
require simultaneous solutions All decision variables are
continuous controllable and non-negative That is x1gt0
x2gt0 xngt0
The objective function
The objective function of each LP problem is a mathematical
representation of the objective in terms of a measurable quantity
7
Operation Research Techniques
such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
8
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
such as profit cost revenue distance etc In its general form it is
represented as
Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn
where Z is the mcasure-of-performance variable which is a function
of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the
contribution of a unit of the respective variable x1 x2 xn to the
measure-of-performance Z The optimal value of the given objective
function is obtained by the graphical method or simplex method
The constraints
There are always certain limitations (or constraints) on the use of
resources eg labour machine raw material space money etc that
limit the degree to which objective can be achieved Such constraints
must be expressed as linear equalities or inequalities in terms of
decision variables The solution of an LP model must satisfy these
constraints
The linear programming method is a technique for choosing the best
alternative from a set of feasible alternatives in situations in which
the objective function as well as the constraints can be expressed as
linear mathematical functions In order to apply linear programming
there are certain requirements to me met
There should be an objective which should be clearly
identifiable and measurable in quantitative terms It could be
for example maximisation of sales of profit minimisation of
cost and so on
8
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
The activities to be included should be distinctly identifiable and
measurable in quantitative terms for instance the products
included in a production planning problem
The resources of the system which arc to be allocated for the
attainment of the goal should also be identifiable and
measurable quantitatively They must be in limited supply The
technique would involve allocation of these resources in a
manner that would trade off the returns on the investment of
the resources for the attainment of the objective
The relationships representing the objective as also the
resource limitation considerations represented by the objective
function and the constraint equations or inequalities
respectively must be linear in nature
There should be a series of feasible alternative courses of action
available to the decision makers which are determined by the
resource constraints
When these stated conditions are satisfied in a given situation the
problem can be expressed in algebraic form called the Linear
Programming Problem (LPP) and then solved for optimal decision
We shall first illustrate the formulation of linear programming
problems and then consider the method of their solution
9
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
ASSUMPTIONS OF LINEAR PROGRAMMING
The following four basic assumptions are necessary for all linear
programming models
Certainty
In all LP models it is assumed that all model parameters such as
availability of resources profit (or cost) contribution of a unit of
decision variable and consumption of resources by a unit of decision
variable must be known and is constant In some cases these may be
either random variables represented by a known distribution (general
or may be statistical) or may tend to change then the given problem
can be solved by a stochastic LP model or parametric programming
The linear programming is obviously deterministic in nature
Divisibility (or continuity)
The solution values of decision variables and resources are assumed
to have either whole numbers (integers) or mixed numbers (integer
and fractional) However if only integer variables are desired eg
machines employees etc the integer programming method may be
applied to get the desired values
It is also an assumption of a linear programming model that the
decision variables are continuous As a consequence combinations of
output with fractional values in the context of production problems
are possible and obtained frequently For example the best solution
to a problem might be to produce 5 23 units of product A and 10 13
units of product B per week
10
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
Although in many situations we can have only integer values but we
can deal with the fractional values when they appear in the following
ways Firstly when the decision is a one-shot decision that is to say
it is not repetitive in nature and has to be taken only once we may
round the fractional values to the nearest integer values However
when we do so we should evaluate the revised solution to determine
whether the solution represented by the rounded values is a feasible
solution and also whether the solution is the best integer solution
Secondly if the problem relates to a continuum of time and it is
designed to determine optimal solution for a given time period only
then the fractional values may not be rounded For instance in the
context of a production problem a solution like the one given earlier
to make 5 23 units of A and 10 units of B per week can be adopted
without any difficulty The fractional amount of production would be
taken to be the work-in-progress and become a portion of the
production of the following week In this case an output of 17 units
of A and 31 units of B over a three-week period would imply 5 23
units of A and 10 units of B per week Lastly if we must insist on
obtaining only integer values of the decision variables we may
restate the problem as an integer programming problem forcing the
solutions to be in integers only
Additively
The value of the objective function for the given values of decision
variables and the total sum of resources used must be equal to the
sum of the contributions (profit or cost) earned from each decision
variable and the sum of the resources used by each decision variable
respectively For example the total profit earned by the sale of two
11
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
products A and B must be equal to the sum of the profits earned
separately from A and B Similarly the amount of a resource
consumed by A and B must be equal to the sum of resources used for
A and B individually
This assumption implies that there is no interaction among the
decision variables (interaction is possible when for example some
product is a by-product of another one)
Finite choices
A linear programming model also assumes that a limited number
of choices are available to a decision-maker and the decision
variables do not assume negative values Thus only non-negative
levels of activity are considered feasible This assumption is indeed
a realistic one For instance in the production problems the output
cannot obviously be negative because a negative production implies
that we should be able to reverse the production process and convert
the finished output back into the raw materials
Linearity (or proportionality)
All relationships in the LP model (ie in both objective function and
constraints) must be linear In other words for any decision variable
j the amount of particular resource say i used and its contribution to
the cost one in objective function must be proportional to its amount
For example if production of one unit of a product uses 5 hours of a
particular resource then making 3 units of that product uses 3 x 5 =
15 hours of that resource
12
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications
there arc some limitations associated with this technique These are
given below Linear programming treats all relationships among
decision variables as linear However generally neither the objective
functions nor the constraints in real-life situations concerning
business and industrial
problems are linearly related to the variables
While solving an LP model there is no guarantee that we will
get integer valued solutions For example in finding out how
many men and machines would be required lo perform a
particular job a non-integer valued solution will be
meaningless Rounding off the solution to the nearest integer
will not yield an optimal solution In such cases integer
programming is used to ensure integer value to the decision
variables
Linear programming model does not take into consideration the
effect of time and uncertainty Thus the LP model should be
defined in such a way that any change due to internal as well as
external factors can be incorporated
Sometimes large-scale problems can be solved with linear
programming techniques even when assistance of computer is
available For it the main problem can be fragmented into
several small problems and solving each one separately
Parameters appearing in the model are assumed to be constant
but in real-life situations they are frequently neither known nor
constant
13
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
It deals with only single objective whereas in real-life situations we
may come across conflicting multi-objective problems In such cases
instead of the LP model a goal programming model is used to get
satisfactory values of these objectives
14
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
APPLICATION AREAS OF LINEAR PROGRAMMING
Linear programming is the most widely used technique of decision-
making in business and Industry and in various other fields In this
section we will discuss a few of the broad application areas of linear
programming
Agricultural Applications
These applications fall into categories of farm economics and farm
management The former deals with agricultural economy of a nation
or region while the latter is concerned with the problems of the
individual farm
The study of farm economics deals with inter-regional competition and
optimum allocation of crop production Efficient production patterns
can be specified by a linear programming model under regional land
resources and national demand constraints
Linear programming can be applied in agricultural planning eg
allocation of limited resources such as acreage labour water supply
and working capital etc in a way so as to maximise net revenue
Military Applications
Military applications include the problem of selecting an air weapon
system against enemy so as to keep them pinned down and at the
same time minimising the amount of aviation gasoline used A
variation of the transportation problem that maximises the total
15
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
tonnage of bombs dropped on a set of targets and the problem of
community defence against disaster the solution of which yields the
number of defence units that should be used in a given attack in
order to provide the required level of protection at the lowest
possible cost
Production Management
Product mix A company can produce several different
products each of which requires the use of limited production
resources In such cases it is essential to determine the
quantity of each product to be produced knowing its marginal
contribution and amount of available resource used by it The
objective is to maximise the total contribution subject to all
constraints
Production planning This deals with the determination of
minimum cost production plan over planning period of an item
with a fluctuating demand considering the initial number of
units in inventory production capacity constraints on
production manpower and all relevant cost factors The
objective is to minimise total operation costs
Assembly-line balancing this problem is likely to arise when
an item can be made by assembling different components The
process of assembling requires some specified sequcnce(s)
The objective is to minimise the total elapse time
16
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
Blending problems These problems arise when a product can
be made from a variety of available raw materials each of
which has a particular composition and price The objective
here is to determine the minimum cost blend subject to
availability of the raw materials and minimum and maximum
constraints on certain product constituents
Trim loss When an item is made to a standard size (eg
glass paper sheet) the problem that arises is to determine
which combination of requirements should be produced from
standard materials in order to minimise the trim loss
Financial Management
Portfolio selection This deals with the selection of specific
investment activity among several other activities The
objective is to find the allocation which maximises the total
expected return or minimises risk under certain limitations
Profit planning This deals with the maximisation of the profit
margin from investment in plant facilities and equipment cash
in hand and inventory
Marketing Management
Media selection Linear programming technique helps in
determining the advertising media mix so as to maximise the
effective exposure subject to limitation of budget specified
exposure rates to different market segments specified minimum
and maximum number of advertisements in various media
Travelling salesman problem The problem of salesman is to
find the shortest route from a given city visiting each of the
specified cities and then returning to the original point of
17
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
departure provided no city shall be visited twice during the
tour Such type of problems can be solved with the help of the
modified assignment technique
Physical distribution Linear programming determines the
most economic and efficient manner of locating manufacturing
plants and distribution centres for physical distribution
Personnel Management
Staffing problem Linear programming is used to allocate
optimum manpower to a particular job so as to minimise the
total overtime cost or total manpower
Determination of equitable salaries Linear programming
technique has been used in determining equitable salaries and
sales incentives
Job evaluation and selection Selection of suitable person for
a specified job and evaluation of job in organisations has been
done with the help of linear programming technique
Other applications of linear programming lie in the area of
administration education fleet utilisation awarding contracts
hospital administration and capital budgeting etc
18
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
Case Study
LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION
NETWORKS PROVISIONING
Abstract
This paper presents a practical proposition for the application of the
Linear Programming quantitative method in order to assist planning
and control of customercircuit delivery activities in
telecommunications companies working with thecorporative market
Based upon data provided for by a telecom company operating in
Brazil the Linear Programming method was employed for one of the
classical problems of determining the optimum mix of production
quantities for a set of five products of that company Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network in face of several
limitations of the productive resources seeking to maximize the
companyrsquos monthly revenue By fitting the production data available
into a primary model observation was made as to what number of
monthly activations for each product would be mostly optimized in
order to achieve maximum revenues in the company The final
delivery of a complete network was not observed but the delivery of
the circuits that make it up and this was a limiting factor for the
study herein which however brings an innovative proposition for the
planning of private telecommunications network provisioning
Introduction
19
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
In the past few years telecommunications have become an input of
great business importance especially for large companies The need
for their own telecommunications network provisioning has been a
constant concern of large- and medium-sized enterprises the world
over Even when a large telecommunications company is outsourced
to operate a customerrsquos network the circuits provisioning of that
network is of utmost importance for the continuation of the business
regarding time and quality Upon delivery of circuits to customers the
large telecom network providers seek ways to reduce their costs by
relying on smaller teams and even more reduced delivery schedules in
an attempt to meet the customerrsquos needs before their competitors do
A data communication network provisioning for instance which in
1999 was activated in 45 days by Europersquos biggest players BTI and
by USArsquos MCI nowadays is
Prepared and delivered to the customer in 21 to 25 days (YANKEE
GROUP 2005) However these are average schedules since urgent
activations are special cases that can be delivered in less than a week
In Brazil the telecommunications industry is facing a scenario with an
excessive number of telecom service providers with an overestimated
demand that marks a scenario of hyper competition Thus the
briefness in activating a service overcomes all of the other features of
that service provisioning also putting aside an adequate planning of
delivery of the products that make up the customerrsquos network and this
prioritization of delivery brings about some loss to the service
providerrsquos cash This paper which is based on data provided by one
telecom provider in Brazil presents an essay that aims to propose a
20
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
simple alternative yet with a solid mathematical basis in order to
ensure there is a marker in the prioritization of customersrsquo circuit
provisioning that aims at the main goal of sales and the business its
profitability
Circuit Activation in Telecom Companies
In order to better understand the proposition of this paper one must
get to know a little about the activation or delivery process of a
telecommunications network provisioning This network presented in
Figure 1 is a set of circuits interlocking through a large telecom
operator backbone several customer environments (sites) from which
he operates his business This process includes all the activities from
the request of a service order by the customer to the provisioning of
the network in operation (the beginning of its commercial running)
going through assembly of every physical part of the network the
configuration of its logical parameters and the running test with
customerrsquos application simulating the day today of the business as
shown in Figure 2
21
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
In Figure 2 it can also be noticed that within the assembly of the
backbonersquos physical part the local access granting activities (2) also
known as lsquolast milersquo equipment acquisition activities for installation
at customersrsquo sites (4) facility allocation activities (communication
channels to be used in the customerrsquos network) within the operatorrsquos
large backbone (1) and customerrsquos network configuration (3) are all
capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customerrsquos network
provisioning
22
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
The lack or poor distribution of such capital brings about a delay in
the provisioning of the networks resulting in loss of profit to the
telecom operator Moreover the random allocation as in a line-up
system ndash FIFO - First In First Out or simply proportional to the
resources available might bring about an undesired delay effect on
large capital inflow to the operator thus representing a problem that
can be solved in a structured way through a Linear Programming
Model
Brazilian Telecom Company
The customer network provisioning division of a big
telecommunications company in the Brazilian market activates on a
monthly basis 3000 circuits of different products (types of network)
which are offered to the market in the following categories Private
Telephone Network Internet Network Intranet Network Low Speed
Data Network and High Speed Data Network Its limited capital and
output capacity allow it to activate only 35 out of the 8500 circuits
backlog monthly This does not pose a problem for the customers
since they accept delivery of their networks in up to 60 days
depending upon the complexity of the network and the kind of
business it is intended for
However since the prices charged for the circuits in each kind of
network are different the company expects that priority be given to
the activation of the circuits that represent higher earnings to the
company Nowadays there is no indicator of how many circuits for
each kind of product must be activated on average per month so that
guidance from the companyrsquos higher management can be followed
23
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
So in a typical month of 2004 a survey was conducted as to the
situation of the companyrsquos circuit delivery and the following results
were attained
Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)
per Service Backlog of a Brazilian Telecom Company in a typical
month
24
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
Where
Service Backlog Circuit delivery orders for each product of the
company
Physical Backlog Number of telecommunications circuits to be
delivered
Financial Backlog Total revenue of the company after circuit
activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on
Dec302004)
Price per Circuit Average unit price of each circuit in each kind of
network
An attempt was made to understand the existing limitations to carry
out circuit delivery in addition to the monthly production capacity
which is already estimated in 3000 circuits per month without any
additional work shift or engagement of temporary labor Five main
25
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
limiters were attained as well as their quantities that are required per
month per type of product as shown in Figure 4 below
Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog
WhereType of Resource Part required for making up a customerrsquos circuit
Access or Last Mile is the linking point between the customerrsquos site
and the operatorrsquos backbone Equipment for the customersrsquo sites are
modems routers or other equipment required for customer
communication on each of his sites Network Facilities are
communications channels within the operatorrsquos backbone that carry
customersrsquo signals from one side of the country or the world to the
other Customer Network Configuration is a set of manual
operations by a technician from the provider company in order to
prepare the operatorrsquos backbone to allow traffic of the customerrsquos
26
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
network circuits through its facilities Other Resources are a set of
minor factors that have been grouped into a single item
PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks
Finally the available amount of each limiting resource in a month was
attained from the physical viewpoint as shown in Figure 5 below
Figure 5 ndash Physical Limit Table for each
resource required for Activations
Based upon these data the network
activation division had to come up with a
marker so that the selection of the circuits
to have priority activation was favorable
to the companyrsquos revenue formation
resulting from the greater amount of
earnings as possible and considering the
existing limitations
The Solution Proposed Through a Linear Programming Model
What the companyrsquos higher management requires can be achieved
through a simple linear programming model which unfortunately is
not used by any telecom company in Brazil despite the amount of
engineers making up their staff The modelrsquos automation is
guaranteed through Microsoft Officersquos Excel application available in
any of the telecom companiesrsquo PCs in Brazil In addition to the
information made available by the company only a calculation of the
27
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
limit of activations in financial values is required for each set of
resource limitations (access equipment network facilities
configurations and others) In order to achieve this we considered
that the maximum amount of activated circuits for each limiting
resource considered separately is the limit figure for each resource
That is for instance if all resources were in abundance and access
was limited to 1200 as shown in Figure 3 the maximum number of
activated circuits would be 1200 equivalent in financial values to
1200 x 140657 = R$ 168788400
Where
140657 is the weighted average of a circuitrsquos price considered the
prices in the fourth column of the Table in Figure 3 against the
weighting figures of the second line of the Table in Figure 4 the line
referring to access By doing the same with the other limiting
resources the limits of the table in Figure 6 are attained
Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations
28
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
By building now the primary linear programming model applied to the
problem proposed and considering that all the data are now
available we get the following elements Object function Max 1048774
154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251
x5
Once what is intended is to maximize the revenue from the prices of
the circuits of each product (see Figure 1)
29
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=
162005760
Once each type of limiting resource (see Figure 2) leads to a
maximum limit of revenue acquisition resulting from circuit delivery
if analyzed separately from the others (see Figure 4)
R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type
of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since
there are no negative activations (Deliveries)
By submitting the Model to the SOLVER function in Microsoftrsquos Excel
application the results shown in Figure 7 are attained
30
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
The most outstanding points shown through the Excelrsquos results are
the optimum outputs for the topic month would be the activation of
1441 private telephone network circuit activations 816 Internet
network circuit activations 200 low speed data network circuit
activations 543 high speed data network circuit activations and
postponing for the following period the activations of the Intranet
network circuits coming to a total of 3000 activations monthly
amounting to a revenue of R$ 476888831 for the company in the
month of study If the same model is calculated bringing production
up to 4000 circuits a month the distribution would be Telephone
networks 1062 Internet 816 Intranet 120 Low Speed Data 1459
High Speed Data 543 for a revenue of R$ 559705312 leaving only
the Telephone and Intranet circuits to be solved in over 30 days as
Figure 8 below shows
31
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
Conclusions and Recommendations
Some conclusions and recommendations can be taken from the
information presented in this paper that help in the day-to-day of a
telecommunications company working with activations (delivery) of
customer corporate network circuits First of all the linear
programming methodology proposes markers for the activations that
further focus on parameters predefined by the companyrsquos
management personnel As for the case presented in this paper if
average figures were to be used by sharing the efforts of the
activations teams per service circuits would be activated that would
add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$
54971831 lower than the revenue made available by following the
linear programming model This means some revenue anticipation of
roughly 25 million American dollars per year On the other hand
within a hyper-competitive environment an output efficiency increase
becomes urgent for any industry or service provider company
Through a Linear Programming Model it gets easy to verify for
instance that by increasing output capacity to 4000 circuits per
month the revenue anticipation is increased by (R$ 559705312 ndash
476888831) R$ 82816481 monthly and this can be enough reason
for the company to hire further human resources to meet this revenue
anticipation
Finally the utilization of statistics-based methodologies is
recommended for output environments even in service providing
aiming at production maximization or even cost reduction It is worth
reminding that the model proposed here presents guidelines for the
priorities not ignoring other underlying factors in prioritizing
32
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
activation such as a customerrsquos urgent need or its category in
segmentation by size or importance The same method used in this
paper can guide the acquisition of resources for circuit activation
rental of third partiesrsquo access or vacation scheduling of the personnel
involved in the provisioning aiming at a more compatible distribution
of human resources throughout the year regarding the demand for
networks and services by customers
33
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
Operation Research Techniques
BIBLIOGRAPHY
The information included in this project is taken from the
reference
Books
Operation Research
Websites
httpwwwyankeegroupcomcustomsearch
search_resultsjspsearch_results
httpwwwwikipediaorg
httpwwwgooglecom
httpwwwmydigitalfccomop-edimportance-fun-work-
613wwwanswerscom
34
- Operation Research Techniques
- Project Report On
- CONTENTS
top related