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Introduction to Operations Research ‐lecture notes (Part 1)
T S P Visit a set of cities/locations and minimize total travel cost
1
4
2
53
Can you guess some of the applications?
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TSP Try to find the best/shortest route?
How many possibilities are there?
1 – 5 – 3 – 4 – 2 – 1 is the optimal route for the travelling salesman.
Duration of the route is 6500 meters.
Locations 1 2 3 4 5
1 0 600 1000 1900 1100
2 600 0 1900 1900 1500
3 1000 1900 0 1700 1200
4 1900 1900 1700 0 1900
5 1100 1500 1200 1900 0
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https://www-m9.ma.tum.de/games/tsp-game/index_en.htmlIsfahan University of Technology - Industrial & Systems Engineering Department Ahmad Reza Pourghaderi - pourghaderi.com
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Introduction to Operations Research ‐lecture notes (Part 1)
Find an allocation of points to vehicles and a set of vehicle routes
ending and beginning at the depot that minimizes either vehicle
distance, number of vehicles, or a combination of the two
Assumes number of vehicles knownIsfahan University of Technology - Industrial & Systems Engineering Department Ahmad Reza Pourghaderi - pourghaderi.com
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There is no clear history that marks the Birth if O.R., it is generally
accepted that the field originated in England during the World War II.
Some say that Charles Babbage (1791-1871) is the Father of O.R
because his research into the cost of transportation and sorting of
mail led to England’s University Penny Post in 1840.
Modern Operations Research originated at the Bowdsey Research
Station in U.K. in 1937 to analyze and improve the working of the
UK’s Early Warning Radar System.
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Given a set of elements
1,2, … , 𝑛 (called the universe) and
a collection 𝑆 of 𝑚 sets
whose union equals the universe,
the set cover problem is to identify
the smallest sub-collection of 𝑆 whose union equals the universe.
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Introduction to Operations Research ‐lecture notes (Part 1)
How to decide on the best locations of medical clinics and emergency vehiclesfor providing maximum Healthcare coverage to a given population?
How many base locations of medical ambulances are needed if the totaldistance from the locations to the hospitals must be less than a given number?
How should radiation treatment be planned for minimizing the treatment timeof a cancer patient?
How should the nurses in a trauma center be scheduled and re-rostered tomaintain an adequate service level even in the worst-case scenario?
Many problems like these need to be addressed in Healthcare, and OperationsResearch (OR) provides numerous methodologies and solution techniques fortackling them.
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HEALTHCARE
Data
Solution
Find a Solution
Tools
Situation
Formulate the Problem
Problem Statement
Test the Model and the Solution
Procedure
Establish a Procedure
Implement the Solution
Construct a Model
Model
Implement a Solution
Goal: solve a problem
• Model must be valid• Model must be tractable• Solution must be useful
OR
May involve current operations orproposed developments due toexpected market shifts
May become apparent throughconsumer complaints or throughemployee suggestions
May be a conscious effort toimprove efficiency or respond to anunexpected crisis
Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.
Data
Situation
Introduction to Operations Research ‐lecture notes (Part 1)
Example: Maximize individual nurse preferences subject to demand requirements, or minimize nurse dissatisfaction costs.
Formulate the Problem
Problem Statement
Data
Situation
Describe system
Define boundaries
State assumptions
Select performance measures
Problem must be translated fromverbal, qualitative terms tological, quantitative terms
A logical model is a series of rules,usually embodied in a computerprogram
Example: Define relationships between individual nurse assignments and preference violations; define tradeoffs between the use of internal and external nursing resources.
Constructa Model
Model
Formulate the Problem
Problemstatement
Data
Situation
A mathematical model is a collection offunctional relationships by which allowableactions are delimited and evaluated.
Many tools are available asdiscussed in this course
Some lead to “optimal” solutions
Others only evaluate candidates trial and error to find “best” courseof action
Example: Collect input data -- nurse profiles and demand requirements; apply algorithm; post-process results to get monthly schedules.
Model
Solution
Find asolution
Tools
Introduction to Operations Research ‐lecture notes (Part 1)
A solution to a problem usually implieschanges for some individuals in theorganization
Often there is resistance to change, makingthe implementation difficult
A user-friendly system is needed
Those affected should go through training
Situation
Procedure
Implement the Procedure
Example: Implement nurse scheduling system in one unit at a time. Integrate with existing HR and T&A systems. Provide training sessions during the workday.
Inventory Control Models:
Operation Research study involves balancing inventory costs against one or more of the
following costs:
Shortage costs.
Ordering costs.
Storage costs.
Interest costs.
This study helps in taking decisions about:
? How much to purchase.
? When to order.
? Whether to manufacture or to purchase i.e., make and buy decisions.
The most well-known use is in the form of Economic Order Quantity (EOQ) equation for finding
economic lot size.
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Waiting Line Models:
It deals with the situations in which queue is formed, e.g. customers waiting for services,
machines waiting for repairmen, and aircrafts waiting for landing strips, etc. These models are
used for minimizing the waiting time and idle time together with the costs associated
therewith.
Waiting line models are of two types:
Queuing theory, which is applicable for determining the number of service facilities and/or
the timing of arrivals for servicing.
Sequencing theory which is applicable for determining the sequence of the servicing.
Replacement Models:
These models are used for determining the time of replacement or maintenance of item, which
may either:
Become obsolete, or
Become inefficient for use, and
Become beyond economical to repair or maintain
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Introduction to Operations Research ‐lecture notes (Part 1)
These models are used to solve the problems arising when:
There are number of activities which are to be performed and there are number of
alternative ways of doing them,
The resources or facilities are limited, which do not allow each activity to be performed
in best possible way. Thus these models help to combine activities and available
resources so as to optimize and get a solution to obtain an overall effectiveness.
Competitive Strategies:
Such type of strategies are adopted where, efficiency of decision of one agency is
dependent on the decision of another agency. Examples of such strategies are game of
cards or chess, fixing of prices in a competitive market where these strategies are termed
as “theory”.
Simulation Models: an experimental method used to study behavior over time.
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Network Models:
This is an approach to planning, scheduling and controlling complex projects.
Transportation Models:
Transportation problems deals with transportation of a product from a number of
sources with limited supplies to number of destinations with specified demands at
the total transportation cost.
The main objective of transportation is to Schedule Shipment from sources to
destinations in such a way so as to Minimize the Total Transportation Cost.
Decision & Game Theory:
Decision Theory is primarily considered with decision making under the conditions
of Risk and Uncertainty
Game Theory is concerned with: Decision Making under Conflicts of Interest
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Operation Research increases the creative capabilities of adecision maker.
It increases the effectiveness of managerial decisions.
Management is most of the time making decisions. It is thus adecision science which helps managers to take better decisions.
Nowadays, business problems have become so complex that it isalmost impossible for a human being to comprehend allimportant factors, OR Techniques can be helpful in suchsituations.
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Introduction to Operations Research ‐lecture notes (Part 1)