Introduction:OR APPROACH TO PROBLEM SOLVING, Observation

Introduction:Model Solution, Implementation of Results >>

Operations Research (MTH601)

Mth 601

Operations Research

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Segment I: Introduction

Lectures 1-3

Operations Research (MTH601)

Background

Technology - the application of science to the everyday Physical World - has, on the

whole, changed our lives greatly for the better, particularly since the time of Industrial

Revolution. Manufacturing industry, which supplies us with and at the same time creates the

wealth, which enables other services to exist, owes its existence to Science and Technology.

Some manufactured items, aircraft for example, are both complex and expensive, and

there are great difficulties, first of all in organizing their manufacture and then, once made, in

using them efficiently. Problems of this latter kind, often called systems problems, were studied

rigorously for the first time by scientists, not in industry but in the management of operations in

the 1939 - 45 war.

A number of teams of eminent scientists were employed by the British Government to

apply their expertise to management and operational problems rather than technical problems.

One such team (the Radar Operational Research team - which gave OR its name) was

responsible for implementing the installation and operation of radar after the technical

development work was complete.

Later on another team examined the relative ineffectiveness of the Allied Forces at

destroying the German U-boats, which were sinking the food convoy ships supplying Britain.

The OR team played an important part in reducing shipping losses and in the ultimate defeat of

the U-boats. With no precedent in the application of Science to the management function, the

scientists were still able to use their scientific approach-collecting information and developing

Operations Research (MTH601)

hypothesis in order to come up with practical plans for the improvement of these wartime

operations.

After the end of the war, the same approach was used with great success in the industrial

and commercial field, developing most rapidly in Britain and the USA, followed by Europe and

the rest of the world. This has provided the basis for the evolution of Operational Research (OR)

as a separate and independent subject of Science. It is not based on any single academic

engineering, social science, economics, statistics and computing but is none of these. Then what

is OR?

DEFINING OPERATIONS RESEARCH:

OR has been defined in various ways and it is perhaps too early to define it in some

authoritative way. However given below are a few opinions about the definition of OR which

have been changed along-with the development of the subject.

In 1946 Morse & Kimbel has defined as;

"OR is a scientific method of providing executive departments with a quantitative

basis for decision regarding the operations under their control"

In 1948 Blackett defined as;

"OR is a scientific method of providing executives with any analytical and

objective basis for decisions"

Another definition is due to Morse who defined in 1948 as;

"The term OR, has here-to fore been used to connote various attempts to study

operations of war by scientific methods. From a more general point of view, OR

Operations Research (MTH601)

can be considered to be an attempt to study those operations of modern society

which involved organizations of men or men and machines".

Later on in 1957, Churchmen Ackoff and Arnoff defined;

"OR is the application of scientific methods, techniques and tools to problems

involving the operations of systems so as to provide those in control of the

operations with optimum solutions to the problem".

In 1958 Saaty defined OR as;

"The art of giving bad answer to problems to which, otherwise, worse answers are

given".

The Operational Research Society of U.K. defines OR as:

"Operational Research is the application of the methods of science to complex

problems arising in the direction and 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 measurements of factors, such as chance and risk, with which to

compare the outcome of alternative decisions, strategies and controls. The

purpose is to help management determine its policies and actions scientifically."

In the USA, where it is called Operations Research, the OR Society of America says

more briefly;

"OR is concerned with scientifically deciding how to best design and operate

man-machine systems, usually under conditions requiring the allocation of scarce

resources".

Operations Research (MTH601)

An even briefer definition might be "Science applied to management", but however, it

might be defined, there is no doubt that OR provides the numerate scientist - of whatever

discipline-with an opportunity to apply the skills of science in the field of Management.

Before proceeding further let us define for the sake of clarity some fundamental terms.

MANAGEMENT, MANAGEMENT SCIENCE AND OR:

MANAGEMENT may be equated with decision-making and control. Government

ministers manage the economy industrialists make decision within their companies and

individual make personal decisions.

MANAGEMENT SCIENCE is the study of problems as abstractions and the application

of the resulting theory to practical situations. Its two fundamental disciplines are behavioral

science and science and quantitative methods.

OPERATIONS RESEARCH (OR) is the application of quantitative methods to decision

making. It formulates problems incisively and assesses the possible consequence of alternative

course of action, so that informed and effective decisions can be taken.

OR APPROACH TO PROBLEM SOLVING:

OR encompasses a logical systematic approach to problem solving. This approach to

problem solving as shown in fig. 1 follows a generally recognized ordered set or steps: (1)

observation, (2) definition of the problems, (3) model construction, (4) model solution, and (5)

implementation of solution results.

OR PROCESS

Operations Research (MTH601)

Observation

The first step in a problem solving exercises in OR is the identification of a problem that

exist in the system. This requires that the system be continuously and closely observed so that

problems can be identified as soon as they occur.

Definition of the Problem

Once it has determined that a problem exists, it must be clearly and concisely defined.

The problem definition includes the limits of the problems and the degree to which it pervades

other organs of the system. A requirement of problem definition is that the goals (or objective)

must be clearly defined which helps to focus attention on what the problem is.

Model Construction

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