Or senting

WELCOME

OPERATIONAL RESEARCH

is a discipline that deals with the application of advanced analytical methods to help make better decisions. It is

often considered to be a sub-field of mathematics.

DEFINITION The application of scientific and especially

mathematical methods to the study and analysis of problems involving complex systems

HISTORY In fact that many experts consider the start of

Operational Research in the III century B.C., during the II Punic War

Thomas Edison made use of Operational Research Second World War by England to solve their complex

war problems. England made OR teams. These teams included expert

mathematicians, statisticians, scientists, engineers, etc. Therefore, United States of America (USA) also started

using OR to solve their war problems. After the war, soon industries and businesses also started using OR to solve their complex management problems.

AREAS OF OR USAGE Scheduling: of aircrews and the fleet for

airlines, of vehicles in supply chains, of orders in a factory and of operating theatres in a hospital.

Facility planning: computer simulations of airports for the rapid and safe processing of travellers, improving appointments systems for medical practice.  

AREAS OF OR USAGE Planning and forecasting: identifying

possible future developments in telecommunications, deciding how much capacity is needed in a holiday business.

Credit scoring: deciding which customers offer the best prospects for credit companies.

AREAS OF OR USAGE Marketing: evaluating the value of sale

promotions, developing customer profiles and computing the life-time value of a customer.

Defence and peace keeping: finding ways to deploy troops rapidly.

SYSTEM ORIENTATION:-OR studies the problem as a whole. it emphasises on over all approach to the system.any activity in one part of an organisation has effect on the other part of the organisation.OR tries to identify all possible interactions in the activities of an organisation and studies their impact

INTERDISCIPLINARY TEAM APPROACH:-OR is interdisplinary in nature. It is performed by a team of scientists drawn from different faculties such as mathematicals,statistics,economics, engineering, management ,physics etc.

Features(or characteristics)of OR(Nature of OR)

SCIENTIFIC APPROACH:-OR uses scientific methods to solve complex problems.OR is a formalised process of reasoning where problems are defined and analysed scientifically

DECISION MAKING:-OR is a decision science which helps management to take better decision.

OPTIMISATION OBJECTIVE:-OR attempts to find the best and optimal solution to a problem using OR techniques.it tries to optimise a well defined function subject to given constraints.

MATHEMATICAL MODELS AND QUANTITATIVE SOLUTION:-OR uses models built by quantitative measurement of variables concerning a given problem and derives a quantitative solution from the model.

BAD ANSWERS TO THE PROBLEM:-OR cannot give perfect answers or solutions to the problems.it merely helps to get bad answers to the problems which otherwise have worse answers.USE OF COMPUTERS:-OR often requires a computer to solve the complex mathematical method.

O.R PROVIDES A TOOL FOR SCIENTIFIC ANALYSER:-OR provides the executives with a more precise description of the cause and effect relationship and risk underlying the business operations in measurable terms.

OR PROVIDES SOLUTION FOR VARIOUS BUSINESS PROBLEMS:-OR techniques are being used in the field of production,procurement, marketing,finance and other allied field.

Importance of OR(functions of OR)

OR HELPS IN MINIMISING WAITING AND SERVICING COSTS:- OR enables the management to decide when to buy and how much to buy.the main object of inventory planning is to achieve balance between the cost of holding stocks and the benefits from stock holding.

OR ASSIST IN CHOOSING AN OPTIMUM STRATEGY:-Linear programming technique is used to allocate resources in an optimum manner in problems of scheduling,product mix and so on.

OR ENABLES PROPER DEVELOPMENT OF RESOURCES:-the OR technique namely PERT enables us to determine the earliest and the latest times for each of the events and activities and helps in identification of critical path.

OR FACILITATES THE PROCESS OF DECISION MAKING:-

Decision theory,decision tree technique,simulation method are used to imitate an operation or process prior to actual performance.

SCOPE OF O.R

IN DEFENCE OPERATIONS To coordinate the function of airforce, navy

and army in a warfare or techniques is applied for their best performance

IN INDUSRTY To co-ordinate the functions in an industry

such as ,production ,advertisment and marketing. The industry depends on OR technique.

IN PLANING To coordinate to the development process of

countries. They depend on OR techniques for future economics social policies

AGRICULTURE To increase the agricultural production they

can easily be solved by the application of OR techniques

IN TRANSPORT OR techniques like monte carlo technique

technique and queuing and linear programing are of grate use in transportation activities

OR AND MODERN BUSINESS MANAGEMENT OR is useful to directing authority It is useful to production management Which is useful to marketing management It is useful to personal management It is very useful to the financial

management

Modeling in O.RModels play a very important in O.R. They are

representation of reality. Models provide descriptions and explanations of the operations of the system that they represent.

“A model in O.R may be defined as an idealized representation of a real life system”

Properties of a good model It should be a simple It should be capable of adjustments with new

formulations without having any significant change in its frame

It should contain very few variables A model should not take much time in its construction

Advantages of a model It describes problems more concisely It provides some logical and systematic approach

to the problem It indicates limitation and scope of the problem It tends to make the over all structure of the

problem more comprehensible It facilitates dealing with the problem in its entirety It enables the use of high-powered mathematical

techniques to analyse the problem It helps in finding avenues new research and

improvements in a system

Disadvantages of a model Models are only an attempt to understand

an operations and should never be considered as absolute in any sense

The validity of any model can only be varified by carrying on experiment and relevant data characteristics

Types of modelsThere are three types of models that are used in O.R

Iconic Models (physical models) Analogue Models(physical models) Symbolic Models (Mathematical models)Iconic model• Iconic models are obtained by enlarging or reducing the size of

the system• They are specified and concrete• They are easy to construct• Eg: photographs,globes.maps etc• It is difficult to manipulate for experimental purpose.It cannot be

used to study the changes in operation of a system.• Difficult to make any modifications,improvements in these

models also adjustments in the changing situation cannot be done.

Analogue models In this models one set of properties is used

to represent another set of properties This models are easier to mainpulate than

iconic models They are less concrete and less specific Eg: lines on a map are analogues of

elevation as they represent the rise and fall of heights.

Symbolic models This type of models are used to represent variables

and the relationship between them They are some kind of mathematical equations . Eg : Inventory models,Allocation

models,Repacement models etc They are most abstract and most general These models are easier to manipulate

experimentally These models yield more accurate results under

manipulation Thus in O.R. symbolic models are used whenever

possible.

General methods of solutions for O.R models

Solving a model consists of finding the values of the controlled variables that optimize the measures of performance, or estimating them approximately. O.R. model solve the following methods.

1. Analytic methods: In these methods all the tools of classical mathematics such as differential calculus and finite difference are available for the solution of a model.

2. Iterative method: whenever the classical method fail, we use iterative procedure. The classical method fail because of the complexity of the constraints or of the number of variables. In this procedure we start with a trail solution and set of rules for improving it.

3. Monte Carlo technique of simulation: the basis of Monte Carlo technique is random sampling of a variable possible values. For this technique, some random numbers are required which may be converted into random variates whose behavior is known from past experience. In short, Monte Carlo technique is concerned with experiments on random numbers and it provides solutions to complicated O.R. problems.

O.R. Technique(Important O.R. models)(Tools of O.R.)

1. Allocation models: allocation models involves the allocation of resources to activates in such a manner that some measures of effectiveness is optimized. Allocation problem can be solved by Linear and Non linear programming techniques. Linear programming technique is used in finding a solution for optimizing a given objective such as maximizing profit or minimizing cost under certain constrains. It is a technique used to allocate scarce resources in an optimum manner in problems of scheduling product mix and so on.

2. Sequencing : These are concerned with placing items in a certain sequence or order for service.

3. Waiting or Queuing theory: These are models that involve waiting for services. In business world several types of interruption occur. Facilitates may break down and therefore repairs may be required. Power failure occur, workers or the needed materials do not show up where and when expected. These cause waiting line problems.

4. Inventory models: these are models with regard to holding resources. The decision required generally entail the determination of how much of resources are to be acquired or when to acquire them. Inventory controls aims at optimum inventory level. Inventory planning is meant to take optimum decision about how much to buy and when to buy.

5. Competitive strategy model(Game model): These are models which arise when two or more people are competing for a certain resources.

6.Decision theory: Decision theory concerned with making sound decisions under conditions of certainty, risk and uncertainty.

7.Net work analysis: Net work model involve the determination of an optimum sequence of performing certain operations concerning some jobs in order to minimize over all time and cost. PERT,CPM and other net work technique such as Gantt chart come under net work model.

8.Simulation: simulation is a technique of testing of model which resembles a real life situation. This technique is used to imitate an operation prior to actual performance.

9.Search models: This model concern itself with search problems. Examples of search problems are 1)Advertising agencies search for customers. 2)Personnel department search for good executives.

10.Replacement theory: These are models concerned with situation that arise when some items (such as machine,electricals etc)need replacement because the same deteriorate with time or may break down completely or may become out of date due to new developments.

Phases of OR (process of OR) (Methodology of OR)

Formulating the problem Constructing the model Deriving the solution Testing the validity Controlling the solution Implementing the result

Formulating the problem:- It consists in identifying, defining and specifying the measures of the components of a decision model. This should yield a statement of the problem’s element that include the controllable variables, the uncontrollable parameters , the restrictions or constraints of the variables and the objectives for defining an improved solution.

Constructing the model:- This phase is concerned with the choice of proper data inputs and design of the appropriate information output . It requires the representation of interrelationship among the elements in terms of mathematical formulae.one or more equations or inequalities is required to express the fact that some or all of the controlled variables can only be manipulated within limits.

Deriving the solution:- The phase deals with mathematical calculation for obtaining solution to the model. A solution to the model means those values of the decision variables that optimise the measures of effectiveness in a model. These are various methods available for obtaining the solution like analytical method, numerical method , and simulation method.

Testing the validity:- A model is said to be valid if it can give a reliable prediction of the system’s performance. A good practitioner of OR realises that his model must have a longer life and must be a good representation of the system and must correspond to reality .In effect,performance of the model must be compared with the policy or procedure that it is meant to replace.

Controlling the solution:- This phase of the study establishes control over the solution of proper feed back of the information variables which deviated significantly. When one or more variables change significantly , the solution goes out of control. In such situations the model be modified accordingly.

Implementing the result:- This phase would basically involve a careful examination of the solution to be adopted and its realities . This phase of OR is primarily executed through the cooperation of both OR experts and those who are responsible for managing and operating the system.

Limitations of OR

OR tries to find out the optimal solution , taking all the factors into account . when there are large number of factors involved , a study of all of them difficult or impossible.

The solution in a problem can be obtained by OR techniques , only if the problem can be quantified. It is not easy or impossible to quantify all elements particularly when they are intangible.

OR is specialist’s job.It requires the effort of Mathematicians and managers put together. When Mathematicians fail to understand the business problem or when the manager fails to understand the working of OR there is gap between who provides solution and who uses the solution.

Greatest difficulty is created by time factor . A solution at the right time will be more useful than a perfect solution arrived late. Therefore there is the problem of choosing between best solution and timely solution.

THANK TO ALL