introduction to operations research ‐ iut‐1397 lecture

Introduction to Operations Research ‐lecture notes (Part 1)

IUT‐1397

© Dr. Ahmad Reza Pourghaderi 1

Ahmad Reza Pourghaderi (Ph.D.)

Assistant Professor of Industrial & Systems Engineering

http://pourghaderi.com/

Introduction to Operational Research

Definition of Operational Research

History of Operational Research

Features of Operational Research

Scope of Operational Research

Methodology/Approaches of Operational Research

Tools/Techniques of Operational Research

Operational Research and Management Decision-Making

Challenges in Operational Research

Isfahan University of Technology - Industrial & Systems Engineering Department Ahmad Reza Pourghaderi - pourghaderi.com

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Our world seems to ever become more complex and

uncertain. Future leaders must be able to act under these

conditions. Optimal decision making in many complex

systems facing big data and high uncertainty is surely

impossible without using computer based advanced

analytical methods.

Operations Research is proven scientific mathematical

processes that enable organizations to turn complex

challenges into substantial opportunities by transforming

data into information, and information into insights that

save lives, save money and solve problems.


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Saving

Lives.S

avingM

oney.S

olvingP

roblems

The In

stitute forOp

eration

s Research

and the

Man

agem

entS

ciences.


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O.R. as termed in USA, Canada, Africa, Australia and Operational

Research as termed in Europe, is a Branch of applied mathematics

that uses techniques and statistics to arrive at Optimal solutions to

solve complex problems.

It is typically concerned with determining the maximum profit,

sale, output, crops yield and efficiency

And minimum losses, risks, cost, and time of some objective

function.

It have also become an important part of INDUSTRIAL

ENGINEERING PROFESSION.


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O.R. is the application of modern methods of mathematical

science to complex problems involving management of large

systems of men, machines, materials, and money in industry,

business, government and defense. The distinctive approach is to

develop a scientific model of the system incorporating

measurement of factors such as chance and risk, to predict and

compare the outcome of alternative decisions, strategies or

controls.


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O.R.

O.R. is a scientific approach to problem solving for management.


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Complete and more stories on:www.informs.org/Impact


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T S P Visit a set of cities/locations and minimize total travel cost

1

4

2

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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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V R P Visit a set of cities/locations and

minimize total travel cost

Assume given locations of N

points, a depot, a matrix of costs

to travel between locations, a

demand for each point, a vehicle

capacity

Can you optimally solve it?

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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It is an Act of winning wars without actually fighting.

Aurther Clark

It is a Scientific Approach to problem solving for executive

management.

H.M. Wagner

It is Art of giving bad answers to problem which otherwise have

worse answers.

T.L. Saaty


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Decision-Making

Scientific Approach

Inter-Disciplinary Team Approach

System Approach

Use of Computers

Objectives

Human Factors


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Every industrial organization faces multifaceted problems to

identify best possible solution to their problems.

OR aims to help the executives to obtain optimal solution with the

use of OR techniques.

It also helps the decision maker to improve his creative and

judicious capabilities, analyze and understand the problem

situation leading to better control, better co-ordination, better

systems and finally better decisions.


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OR applies scientific methods, techniques and tools for the

purpose of analysis and solution of the complex problems.

In this approach there is no place for guesswork and the person

bias of the decision maker.


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Basically the industrial problems are of complex nature and

therefore require a team effort to handle it.

This team comprises of scientist, mathematician and

technocrats. Who jointly use the OR tools to obtain a optimal

solution of the problem. They tries to analyze the cause and

effect relationship between various parameters of the problem

and evaluates the outcome of various alternative strategies.


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The main aim of the system approach is to trace out all

significant and indirect effects for each proposal on all sub-

system on a system and to evaluate each action in terms of

effects for the system as a whole.

The inter-relationship and interaction of each sub-system can be

handled with the help of mathematical/analytical models of OR

to obtain acceptable solution.


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The models of OR need lot of computation and therefore, the use of

computers becomes necessary.

With the use of computers it is possible to handle complex problems

requiring large amount of calculations.

The objective of the operations research models is to attempt and to

locate Best or Optimal Solution.


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Operational Research always try to find the best and optimal

solution to the problem.

For this purpose objectives of the organization are defined and

analyzed. These objectives are then used as the basis to

compare the alternative courses of action.


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In deriving, Quantitative Solutions we do not consider human

factors, which doubtlessly play a great role in the problems.

So, study of O.R. is incomplete without study of human factors.


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The scope of OR is not only confined to any specific agency like defense

services but today it is widely used in all industrial organizations. It attempts to

resolve the conflicts of interest among the components of organization in a way

that is best for the organization as a whole. It can be used for solving different

types of problems, such as:

Finance, Budgeting and Investment:

Cash flow analysis, long range capital requirement, investment portfolios, dividend

policies, claim procedure, and credit policies.

Marketing:

Product selection, pricing, competitive actions, number of salesmen, frequencies of

calling on, and advertising strategies with respect to cost and time.


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Purchasing:

Buying policies, varying prices, Determination of quantities and timing of purchases,

Bidding policies, Replacement policies, and Exploitation of new material resources.

Production Management:

Physical distribution: Location and size of warehouses, distribution centers and retail

outlets, distribution policies.

Facilities Planning: Number and location of factories, warehouses etc. Loading and

unloading facilities.

Manufacturing: Production scheduling and sequencing stabilisation of production,

employment, layoffs, and optimum product mix.

Maintenance policies, crew size.

Project scheduling and allocation of resources.


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Personnel Management:

Mixes of age and skills, shift scheduling, Education planning, Recruiting policies, and Job

assignments.

Research and Development:

Areas of concentration for R&D, Reliability and alternate decisions, Determination of

time-cost trade off and control of development projects.

Healthcare Operations Management:

Operating room planning and scheduling, resource planning for equipment, rooms and

staff, medical Inventory management, planning and managing emergency services, Organ

donation and transplant, modeling spread of epidemics and planning response,

treatment method selection, financial planning and pricing in health care


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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


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Define variables

Define constraints

Identify data requirements

Example: Maximize individual nurse preferences subject to demand requirements, or minimize nurse dissatisfaction costs.


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


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


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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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Allocation/Assignment Models:

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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Magnitude of Computation

Non-Quantifiable Factors

Distance between User and Analyst

Time and Money Costs

Implementation


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Operations research models try to find out optimal solution taking

into account all the factors.

These factors are usually enormous in real management problems.

Expressing them in quantity and establishing relationships among

these, Require voluminous calculations which can be handled only

by computers.

Sometime we need to use High Performance Computers (HPC)

Sometimes even using HPCs cannot provide satisfactory results.


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OR provides solution only when all elements related to a problem can

be quantified.

All relevant variables do not lend themselves to quantification.

Factors which cannot be quantified, find no place in OR study.

Some of qualitative factors such as emotional factors are very

difficult (some say impossible but I dot believe in them) to be

quantified.


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OR being specialist’s job requires a mathematician or statistician or

ideally an Industrial Engineer, who might not be aware of the business

problems.

Similarly, a manager fails to understand the complex working of OR.

Thus there is a gap between the two. Management itself may offer a lot

of resistance due to conventional thinking.


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When basic data are subjected to frequent changes, incorporating

them into the OR models is a costly proposition.

Moreover, a fairly good solution at present may be more desirable

than a perfect OR solution available after sometime. The

computational time increases depending upon the size of the

problem and accuracy of results desired.


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Implementation of any decision is a delicate task. It must take into

account the complexities of human relations and behaviors.

Sometimes, resistance is offered due to psychological factors

which may not have any bearing on the problem as well as its

solution.


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introduction to operations research ‐ iut‐1397 lecture

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