operations-research-1229480696777816-1

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OPERATIONS RESEARCH

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Emmanuel Mazomola

AN OVERVIEW


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After reading the present module, learner will be able to:

General Objectives:

Understand the concept of Operations Research

Know Phases and Process of Operations Research

Specific Objectives:

Name the basic terms related with O.R

Define basic terms related with OR.

Define Operation Research

Describe the phases of O.R.

Draw the flow chart of O.R. approach.

List out the various techniques of O.R. Give application fields of various techniques.

List out the components of mathematical model.

State advantages and limitations of O.R.

Identify the various application fields of O.R.


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Module -Table of Contents

Introduction Origin

Practice Task

Phases and Process of OR

Practice Task

Techniques of OR

Advantages and Disadvantages Of OR

Applications of OR Practice Task

References


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IntroductionHello learners, this is first self-learning module on Basics of Operations

Research.Today, almost every large organization or corporation in developed nationsas well as to some extent in developing countries has executive applyingoperations research, and in government the use of operations research hasspread from military to widely varied departments at all levels.

Availability of faster and flexible computing facilities and the number ofqualified OR professionals has enhanced the acceptance and popularity ofthe discipline. The growth of OR has not been limited to the USA and theUK, now it has reached to many countries including India.

India was one of the first few countries who started using OR. In 1949, thefirst OR unit was established in the Regional Research Laboratory atHyderabad. Today, OR is a popular subject in management, mechanicalengineering and the mathematics.

So for engineers, the knowledge of OR is very essential not just forplacement but also for career growth. This is first module definesOperations Research and gives a brief historical background of it. It alsogives insight into the approaches and tools of OR and identify theapplication areas in which OR has used successfully.

ALL THE BEST for this wonderful Journey.


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ORIGIN The ambiguous term Operations Research (OR) was coined

during world war II, when the British Military Management called

upon a group of scientists together to apply a scientific approachto the study of military operations to win the battle.

Operations Research originated in Great Britain during World War IIto bring mathematical or quantitative approaches to bear on militaryoperations.

The main objective was to allocate the scarce resources in aneffective manner to the various military operations and to theactivities within each operation.

The effectiveness of operations research in military spread in itto other government department and industry.

Due to the availability of faster and flexible computing facilities

and the no. of qualified O.R. professionals, it is now widely usedin military, business, industry, transportation, public health etc. Since its birth in the 1940's, OR has been widely recognized as an

important approach to decision-making in the management of all aspects ofan organization.


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TIME STARVED EXECUTIVESARE MAKING BOLDER

DECISIONS WITH LESS RISK

AND BETTER OUTCOMES.THEIR SECRET

OPERATION RESEARCH


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INTRODUCTION

It is concerned with co-ordinating and controllingthe operations or activities within theorganization.

O.R. can be regarded as the mathematical and

quantitative techniques to substantiate thedecisions being taken.

O.R. takes tool from subjects like statistics,mathematics, engineering, economics,

psychology etc. and uses them to know theconsequences of possible alternative actions.

Operations research (OR) is a disciplineexplicitly devoted to aiding decision makers.


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OPERATIONS

The activities carried out in anorganization related to attaining its

goals and objectives.


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RESEARCH

The process of observation and testingcharacterized by the scientific method. The

steps of the process include observing thesituation and formulating a problemstatement, constructing a mathematicalmodel, hypothesizing that the model

represents the important aspects of thesituation, and validating the model throughexperimentation.


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ORGANIZATION

The society in which the problem arises or

for which the solution is important. The

organization may be a corporation, a

branch of government, a department

within a firm, a group of employees, or

perhaps even a household or individual.


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DECISION MAKER

An individual or group in theorganization capable of proposing

and implementing necessary actions.


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1.The process of observation and testing characterized by the scientific

method.

(True/False)

Practice Task


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Yes, you are true. Scientific methods are employed for observation and

test the situations.

Now Answer the Next Question.


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No, you are wrong. Unscientific methods leads to confusion and donotgive reliable and valid solutions.



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2.Operations Research (OR) was coined during world war II, when the

_ _ _ _ _ _ _ _ _ _Management called upon a group of scientists.

Practice Task


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Ans. British Military

You are excellent! Now you learn the next input.


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MAKING DECISIONS OR

TAKING ACTIONS IS

CENTRAL TO ALL

OPERATION RESEARCH

APPLICATIONS


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DEFINITIONS

OR is a scientific method of providing executivedepartments with a quantitative basis fordecisions regarding the operations under theircontrol.Morse & Kimball

Operations research is a scientific approach toproblem solving for executive management. H.M. Wagner

Operations research is an aid for the executivein making this decisions by providing him withthe needed quantitative information based onthe scientific method of analysis. C. Kittel


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Nature of O.R. Characteristics

Inter-disciplinary team approach

Systems approach

Helpful in improving the quality of solution

Scientific method

Goal oriented optimum solution

Use of models

Require willing executives

Reduces complexity


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PHASES

OPERATIONS RESEARCH


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1.Recognize the Problem


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1. Recognize the Problem

Decision making begins with a situation in which aproblem is recognized.

The problem may be actual or abstract, it mayinvolve current operations or proposed expansions

or contractions due to expected market shifts, it maybecome apparent through consumer complaints orthrough employee suggestions, it may be aconscious effort to improve efficiency or a responseto an unexpected crisis.

It is impossible to circumscribe the breadth ofcircumstances that might be appropriate for thisdiscussion, for indeed problem situations that areamenable to objective analysis arise in every area ofhuman activity.


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2. Formulate the Problem

At the formulation stage,

statements of objectives, constraints on solutions,appropriate assumptions, descriptions of processes,data requirements, alternatives for action and metricsfor measuring progress are introduced.

Because of the ambiguity of the perceived situation,the process of formulating the problem is extremelyimportant. The analyst is usually not the decisionmaker and may not be part of the organization, socare must be taken to get agreement on the exactcharacter of the problem to be solved from those whoperceive it. There is little value to either a poor solutionto a correctly formulated problem or a good solution toone that has been incorrectly formulated.


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3. Construct a Model

A mathematical model is a collection of functional relationships by whichallowable actions are delimited and evaluated. Although the analyst wouldhope to study the broad implications of the problem using a systemsapproach, a model cannot include every aspect of a situation.

A model is always an abstraction that is, by necessity, simpler than thereality.

Elements that are irrelevant or unimportant to the problem are to beignored, hopefully leaving sufficient detail so that the solution obtained withthe model has value with regard to the original problem.

The statements of the abstractions introduced in the construction of themodel are called the assumptions. It is important to observe thatassumptions are not necessarily statements of belief, but are descriptions ofthe abstractions used to arrive at a model. The appropriateness of the

assumptions can be determined only by subsequent testing of themodels

validity.

Models must be both tractable -- capable of being solved, and valid --representative of the true situation. These dual goals are often contradictoryand are not always attainable. We have intentionally represented the modelwith well-defined boundaries to indicate its relative simplicity.


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4. Find a Solution(1)

The next step in the process is to solve the model toobtain a solution to the problem. It is generally truethat the most powerful solution methods can beapplied to the simplest, or most abstract, model.

Some methods can prescribe optimal solutions while

other only evaluate candidates, thus requiring a trialand error approach to finding an acceptable course ofaction.

It may be necessary to develop new techniquesspecifically tailored to the problem at hand. A model

that is impossible to solve may have been formulatedincorrectly or burdened with too much detail. Such acase signals the return to the previous step forsimplification or perhaps the postponement of thestudy if no acceptable, tractable model can be found.


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4. Find a Solution(2)

Of course, the solution provided by thecomputer is only a proposal. An analysis doesnot promise a solution but only guidance to thedecision maker.

Choosing a solution to implement is theresponsibility of the decision maker and not the

analyst. The decision maker may modify thesolution to incorporate practical or intangibleconsiderations not reflected in the model.


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5. Establish the Procedure(1)

Once a solution is accepted a procedure must bedesigned to retain control of the implementationeffort.

Problems are usually ongoing rather than unique.

Solutions are implemented as procedures to beused repeatedly in an almost automatic fashionunder perhaps changing conditions.

Control may be achieved with a set of operating

rules, a job description, laws or regulationspromulgated by a government body, or computerprograms that accept current data and prescribeactions.


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5. Establish the Procedure(2)

Once a procedure is established (and implemented),the analyst and perhaps the decision maker areready to tackle new problems, leaving the procedureto handle the required tasks.

But what if the situation changes? An unfortunate result of many analyses is a remnantprocedure designed to solve a problem that nolonger exists or which places restrictions on anorganization that are limiting and no longer

appropriate. Therefore, it is important to establish controls that

recognize a changing situation and signal the needto modify or update the solution.


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6. Implement the Solution

A solution to a problem usually implies changes for someindividuals in the organization. Because resistance tochange is common, the implementation of solutions isperhaps the most difficult part of a problem solving

exercise. Some say it is the most important part. Although not

strictly the responsibility of the analyst, the solutionprocess itself can be designed to smooth the way forimplementation.

The persons who are likely to be affected by thechanges brought about by a solution should take part, orat least be consulted, during the various stages involvingproblem formulation, solution testing, and theestablishment of the procedure.


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The OR Process

Combining the steps we obtain the complete ORprocess.

In practice, the process may not be well definedand the steps may not be executed in a strictorder. Rather there are many loops in the process,

with experimentation and observation at each stepsuggesting modifications to decisions madeearlier.

The process rarely terminates with all the looseends tied up. Work continues after a solution isproposed and implemented. Parameters andconditions change over time requiring a constantreview of the solution and a continuing repetitionof portions of the process.


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O.R. APPROACH


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1. Write the name of the phases of O.R.

Check your answer.

Practice Task


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Ans. Judgment Phase

Research Phase

Action Phase



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2. Decision making begins with a situation in which a problem is

recognized. (True/False)

Practice Task


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Yes, it is true. Problem is firstly identified then other phases follows.



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No, you are wrong. If problem is not recognized at first, there will

be ambiguity in the process of finding optimum solution.



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3. Why formulation of problem is necessary to solve O.R. problem?

Check your answer.

Practice Task


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Ans. 3 Because of the ambiguity of the perceived situation, the process

of formulating the problem is extremely important.



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Q 4.Is initial solution of the problem is always optimum?(True/False)

Practice Task


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Yes, you are right. Always all the solutions come are not

optimum, it is only guide us to tell in which direction the

solution can be optimum.



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No, you are wrong. The initial solution may or may not be optimum.There can other alternative or better solutions available.



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Q 5. Resistance to change is common, when the solution isimplemented in the organisation.

(Yes/No)

Practice Task


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Yes, you are right. During the time of new solution is implemented, the

personnel of the organization resist to change the situations very often.



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No, you are wrong. Human resource in the organization creates hurdles

in changing the existing situations even in exist conditions are not

conducive.



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TECHNIQUES OF OR(1) Linear programming- It has been used to solve problems

involving assignment of jobs to machines, blending, productmix, advertising media selection, least cost diet, distribution,transportation and many others.

Dynamic programming- It has been applied to capitalbudgeting, selection of advertising media, cargo loading and

optimal routing problems.

Waiting line or queuing theory- It has been useful to solveproblems of traffic congestion, repair and maintenance ofbroken-down machines, number of service facilities,

scheduling and control of air-traffic, hospital operations,counter in banks and railway booking agencies.

Inventory control / planning- These models have been usedto determine economic order quantities, safety stocks, reorderlevels, minimum and maximum stock level.


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TECHNIQUES OF OR(2) Decision theory- It has been helpful in controlling

hurricuanes, water pollution, medicine, space exploration,

research and development projects.

Network analysis (PERT& CPM)- These techniques havebeen used in planning, scheduling and controllingconstruction of dams, brides, roads and highways anddevelopment & production of aircrafts, ships, computers etc.

Simulation- It has been helpful in a wide variety ofprobabilistic marketing situations.

Theory of replacement- It has been extensively employed todetermine the optimum replacement interval for three types ofreplacement problems:

i) Items that deteriorate with time.

ii) Items that do not deteriorate with time but fail suddenly.

iii) Staff replacement and recruitment.


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What is a Mathematical Model? The majority of practical decision problems are

described in very vague terms. Therefore, a most-important step in a scientific or quantitative analysisof a problem is to formulate a model that adequatelycaptures the essence of a problem. The result ofsuch a formulation, or an abstraction, is called amathematical optimization model.

Generally speaking,

a mathematical optimization model has thefollowing typical components:

a set of decision variables

an objective function, expressed in terms of thedecision variables, that is to be minimized ormaximized

a set of constraints that limit the possible values of

the decision variables


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ADVANTAGES

Provides a tool for scientific analysis. Provides solution for various business problems.

Enables proper deployment of resources.

Helps in minimizing waiting and servicing costs.

Enables the management to decide when to buyand how much to buy?

Assists in choosing an optimum strategy.

Renders great help in optimum resource allocation.

Facilitates the process of decision making. Management can know the reactions of the

integrated business systems.

Helps a lot in the preparation of future managers.


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LIMITATIONS The inherent limitations concerning mathematical

expressions High costs are involved in the use of O.R.

techniques

O.R. does not take into consideration the intangible

factors O.R. is only a tool of analysis and not the complete

decision-making process

Other limitations

Bias

Inadequate objective functions

Internal resistance

Competence

Reliability of the prepared solution


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Application Fields

Industry

Defense

Planning

Agriculture

Public utilities


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Ques. 1Assignment of jobs to machines problems can besolved by linear programming.

True

Practice Task


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Yes, you are right. Assignment Problems is solved with the help

of linear programming techniques.

You are excellent! Now you are at the end.


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No, you are wrong. Assigning the machines problems can bestbe solved by linear programming techniques.

You are excellent! Now you are at the end.


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References

Operations Research : An Overview

Lecture by Mr. P. Ghosal,Department of

Information Technology,Bengal

Engineering & Science University,Shibpur, February 14, 2007.

Operations Research Simplified, chapter-1

from www.universalteacher.com


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THANKS

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