Lecture No# 1
Operational Research
It is a scientific
approach to determine the optimum solution to a decision problem under the
restriction of limited resources using the mathematical techniques to model
analyze and solve the problem.
OR
Operational Research
(O.R) is an art of wining wars without actual fighting.
(Arthur Clark)
OR
It is a scientific
approach to problem solving for executive achievement.
(H.M Wagner)
History of Operational
Research
O.R came into
existence during world war two when the British
and American military management called upon a group of scientist with diverse.
Educational Background
namely Biology, Physics, Mathematics, Psychology etc. to develop and
apply scientific approach to deal with the strategic and technical problem of
various military operations.
The object was to
allocate scare resources in an effective manner to various military operations
and to the activities within each operation.
The name O.R came
directly from context in which it was used and developed by research and
military operations.
During the 1950’s O.R achieved recognition as a subject for study
in the universities increasing importance for the students of management,
public administration, Economics and commerce etc.
Today O.R is also
widely used in regional planning transportation, public health and
communication etc. besides military and industrial operations.
In India O.R came
into existence in 1949 with the opening of an
O.R unit at RRL (Regional Research Laboratory )
at Hyderabad and also in the defense science Laboratory at Delhi , which
developed itself to the problems of stores, purchase and planning for national
planning and survey an O.R unit was established in 1953
at the Indian statistical institute,Culcutta .
In 1957 O.R society of India was formed. All most all
universities and institutions in India are offering the input O.R in their Curriculum.
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Lecture No# 2
Characteristics of
Operational Research
ØUse of interdisciplinary(Group of people) Team:-
When
we are solving a problem with the help of O.R it involves a number of variables
and constraints. A single person cannot study an analyze the problem carefully.
So we require a group of people that they can study and analyze the problem carefully.
Then that group after analyzing the problem uses their skills to get better solutions.
By this reduce the chance of wrong decision.
Ø Complete system Orientation
If
we consider a company and a business it has a separate system and each system
has sub-separate system. The decision of single sub-system effects the others
sub-system to solve any problem. We consider a whole system .We also say that
operation Research is a system approach not an individual approach.
Ø Involvement of scientific Method
Scientific
method contains logics and empirical (Hatmi) relation belongs to pass
experiments with the help of this. we Remove the irrelevant assumption and
result from given problem which does not have any effect.
Ø Improvement in Quality
of decision
By
using scientific approach we get logical and significant results are solution
of problem. By analyzing the effects of problem we select the optimal solution
by using this optimal solution. We improve the Quality of decision.
Ø Uncovering hidden Problems
While
solving the problem we observe that there are some problems which have most
effect actual problems. We use different techniques after analyzing such hidden
problems to solve them so that their effects on actual problem can be reduced.
Phases of Operational
Research
1.
Pre-Modeling phase
The problem which we want to be
solve is clearly identified ,Because if problem is not clearly identified
cannot give the accurate solution .We want to format the problem in standard
form having object function ,factors effecting the problems and constraints.
2.
Modeling phase
In this phase first we do the
formulation of problem. We convert the standard form of model into mathematical
model ,Then decision variable , constraints and objective function also
converted into mathematical model .we have sets of equation for effective
measure of objective function .The effective measurement is change of
parameters on objective function .To solve any problem we need sufficient data
which is to be collected from standard data book. The next step is the
identification of possible alternate data by applying scientific /O.R
techniques. We get alternative solution .This characteristics of operational
Research that we get alternative solutions for one problem .That is the reason
that operational Research is also called optimization tool.
3.
Implementation phase
This phase consist of solution
interpretation and model validation. By solving the mathematical model of given
problem by using O.R techniques .We get different solution, we select only one
solution .We check the best solution for optimality of objective function, that
solution is called best optimal solution and the process of finding the best
solution is called model validation .We apply the best solution to real
solution if it fails to get the required result we change the solution to get
desired result.
Scope of O.R
Ø
Industry
Ø
Planning
Ø
Defense
Ø
Public
utilities
Ø
Agriculture
Ø
Management
Limitations of O.R
Ø
Lack of
Qualitative Facilities
Ø
Limited
factor Consideration
Ø
Specific
categories of Problem
Ø
Resistance
of employees and management
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Assignment No# 1
Objective function:
It
is a linear function of decision variables z=x1+x2 is the most typical form of
objective functions are maximize f(x) or minimize f(x).
In
short word (Decision variable are those which
decides that where function is maximum and where function is minimum)
Constraints:
These
are the linear equation arising out of practical limitations. The mathematical
form of constraints are f(x)<=b or f(x)=>b or f(x)=b.
Feasible Solution:
A
non-negative solution which satisfies all the constraints is known as feasible solution. The Region comprising all feasible
solutions is referred to as feasible region.
Optimal solution:
The
solution where the objective function is maximize or minimizes is known as optimal solution.
