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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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