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OPERATIONS

RESEARCH

Chapter one: Introduction

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Operations Research (OR) started just before

World War II in Britain with the

establishment of teams of scientists to study

the strategic and tactical problems involved

in military operations. The objective was to

find the most effective utilization of limited

military resources by the use of quantitative

techniques.

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Following the war, numerous peacetime

applications emerged, leading to the use of

OR and management science in manyindustries and occupations.

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Operations research is the application of

mathematical techniques and scientific

principles to management problems to help

managers make better decisions.

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The five function s of operation

research are objectives, scientific

approach, interdisciplinary team work,

use of computers, and decision making.

Making decisions or taking actions is

central to all operations researchapplications.

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There are various techniques used in OR

such as, Linear Programming, ProbabilityTheory, Transportation Algorithm,

Assignment problems, Queuing theory, etc.

Operations research (OR) has application in

forecasting, inventory management,

production planning , capital budgeting,

capacity planning, and other important areasof management decision making.

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Problem solving can be eitherqualitative orquantitative.

In qualitative problem solving intuition andsubjective judgment are used.

Quantitative analysis tend to be more objectiveand will include only information that can be

quantified

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Qualitative approach is used when the

problem is fairly simple and familiar, the costinvolved is not much and immediate decision

are needed.

Quantitative approach is used when problem

is complex and not familiar, cost involved is

substantial and enough time is available toanalyze the problem.

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1.2. Model is an abstraction of a reality.

Models are classified as

1. Physical(iconic) model: are the least abstract.

They are physical models that look like reality.such as model of an airplane, layout

drawing of a factory, glob, etc.

2. Analogue models: Physical models which are

more abstracts than iconic models such as,

graph, flowcharts, Gantt charts, cause-effect

diagram etc.

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3. Mathematical models( symbolic models):

are the most abstract models which usuallyrepresent a problem in a form of mathematical

equations or in a set of mathematical

relationships. These mathematicalrelationships are made up of symbols and

numbers.

variable within a model is amathematical symbol that can take

on different values. Variables are 10


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parameter is a constant value that is mostly a

coefficient of a variable in a mathematical

equation / relationship.

Constants are fixed values not subject to

variation generally represented by numbers.

While variables can take on different values.

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Example: Suppose a company produces

three different items: item A, item B anditem C. The profit obtained from each item

A is Birr 20, from each item B is Birr 32 and

from each item C is Birr 18. Write anequation ( a mathematical model) which can

be used to compute profit.

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The total profit depends on the number of each

item sold. Hence the number of items sold is

represented by variables while the profit on

each item is a constant that doesnt vary.

Let x1 :number of units of item A soldx 2 : number of units of item B sold

x3 : number of units of item C sold

Profit = 20 x1 +32x2 +18x313


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In this example x1, x 2, x 3 are called

decision variables since managers can

give decisions on values of this variables.

However there can be other variables

such as weather, government decisions

that are not under the control of managersbut can affect the profit. Such type of

variables are called uncontrollable

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1.3. The ManagementScience approach

Management science encompasses a

logical, systematic approach to problem

solving, which closely parallels what isknown as the scientific method for

attacking problems. This approach,

follows an ordered series of steps: (1)definition of the problem, (2) model

construction, (3) model solution(analysis)

and (4) implementation of solution. 15


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PROBLEM

DEFINITION

MODEL

CONSTRUCTION

ANALYSIS

IMPLEMENTATIO

N AND FOLLOW-UP

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