Introduction to Operations Research

INTRODUCTION TO
OPERATIONS RESEARCH

INTRODUCTION TO
OPERATIONAL RESEARCH
 Operational Research is a systematic and analytical
approach to decision making and problem solving.
 O.R. as termed in USA, Canada, Africa, Australia
and Operational Research as termed in Europe, is
an Branch of applied mathematics that uses
techniques and statistics to arrive at Optimal
solutions to solve complex problems.

INTRODUCTION TO
It is typically concerned with determining the
maximum profit, sale, output, crops yield and
efficiency and minimum losses, risks, cost, and
time of some objective function. It have also
become an important part of INDUSTRIAL
ENGINEERING PROFESSION.

Some of the PRIMARY TOOLS used
by operation researchers are-
STATISTICS
GAME THEORY
PROBABILITY THEORY, etc.

HISTORY OF
 There is no clear history that marks the Birth
if O.R., it is generally accepted that the field
originated in England during the World War II.
Some of them says that Charles Babbage (1791-
1871) is the Father of O.R because his research
into the cost of transportation and sorting of
mail led to England’s University Penny Post in
1840.

HISTORY OF
 Modern Operations Research originated at the
Bowdsey Research Station in U.K. in 1937 to
analyse and improve the working of the UK’s
Early Warning Rador System.
 During the Second World War about 1000 Men
and Women were engaged to work for British
Army.
 After World War II, Military Operational
Research in U.K. became Operational Analysis
(OA) within the U.K. Ministry of Defence with
expanded techniques and graving awareness.

IN INDIA
The Operational Research Society of India was
founded in 1957 to provide a forum for the
Operational Research Scientists as well as an
avenue to widen their horizon by exchange of
knowledge and application of techniques from
outside the country. The Society is affiliated to
the International Federation of Operational
Research Societies (IFORS).

IN INDIA
The Headquarters of the Society is located in
Kolkata at 39, Mahanirvan Road, Kolkata
700029, India. At present the Society has 12
Operating Chapters located
in Agra,Ahmedabad, Ajmer, Bangalore,
Chennai, Delhi, Durgapur,
Jamshedpur, Kolkata, Madurai,
Mumbai and Tirupati.

IN INDIA
The Objectives of the Society comprise
advancement of, conducting of research in,
study of, promotion and propagation of
knowledge in Operational Research and Allied
Techniques through exchange of information, as
well as establishment, improvement and
maintenance of professional and academic
standards of work known as Operational
Research.

IN INDIA
Contribution to the Society towards attainment
of these objectives is eligible for exemption of
income tax under Section 80(G)(5)(vi) of the
Income Tax Act 1961.
The Society Publishes a quarterly
journal OPSEARCH, which brings out high
quality and state of the art papers in Operational
Research.

IN INDIA
In order to provide opportunity to professionals
and students to equip themselves with the
knowledge and usage of the science of
Operational Research, the Society is conducting
an examination on Graduate Diploma in
Operational Research since 1973.

DEFINITION OF
It is an Act of winning wars without actually
fighting.
-Aurther Clark
It is a Scientific Approach to problem solving for
executive management.
-H.M. Wagner
It is Art of giving bad answers to problem which
otherwise have worse answers.
-T.L. Saaty

FEATURES OF
Decision-Making
Scientific Approach
Inter-Disciplinary Team Approach
System Approach
Use of Computers
Objectives
Human Factors

DECISION MAKING
Every industrial organisation faces multifacet
problems to identify best possible solution to their
problems.
OR aims to help the executives to obtain optimal
solution with the use of OR techniques.
It also helps the decision maker to improve his
creative and judicious capabilities, analyse and
understand the problem situation leading to
better control, better co-ordination, better
systems and finally better decisions.

SCIENTIFIC APPROACH
OR applies scientific methods, techniques and
tools for the purpose of analysis and solution of
the complex problems.
In this approach there is no place for guesswork
and the person bias of the decision maker.

INTER-DISCIPLINARY
TEAM APPROACH
 Basically the industrial problems are of
complex nature and therefore require a team
effort to handle it.
 This team comprises of scientist, mathematician
and technocrats. Who jointly use the OR tools to
obtain a optimal solution of the problem. They
tries to analyse the cause and effect relationship
between various parameters of the problem and
evaluates the outcome of various alternative
strategies.

SYSTEM APPROACH
The main aim of the system approach is to
trace out all significant and indirect effects for
each proposal on all sub-system on a system
and to evaluate each action in terms of effects
for the system as a whole.
The inter-relationship and interaction of
each sub-system can be handled with the help
of mathematical/analytical models of OR to
obtain acceptable solution.

USE OF COMPUTERS
 The models of OR need lot of
computation and therefore, the use of
computers becomes necessary.
 With the use of computers it is
possible to handle complex problems
requiring large amount of calculations.
 The objective of the operations
research models is to attempt and to
locate Best or Optimal Solution.

OBJECTIVES
Operational Research always try to find
the best and optimal solution to the
problem.
For this purpose objectives of the
organisation are defined and analysed.
These objectives are then used as the
basis to compare the alternative courses
of action.

HUMAN FACTORS
In deriving, Quantitative Solutions we do
not consider human factors, which
doubtlessly play a great role in the
problems.
So, study of O.R. is incomplete without
study of human factors.

SCOPE OF
The scope of OR is not only confined to any specific
agency like defence services but today it is widely used in
all industrial organisations.
It can be used to find the best solution to any problem be
it simple or complex. It is useful in every field of human
activities. Thus, it attempts to resolve the conflicts of
interest among the components of organization in a way
that is best for the organisation as a whole.

The main fields where OR is
extensively used are
National Planning and Budgeting
Defence Services
Industrial Establishment and Private
Sector Units
R & D and Engineering

NATIONAL PLANNING AND
BUDGETING
OR is used for the Preparation of-
 Five Year Plans
 Annual Budgets
 Forecasting of Income and Expenditure
 Scheduling of Major Projects of National Importance
 Estimation of GNP
 GDP
 Population
 Employment and Generation of Agriculture Yields,
etc.

DEFENCE SERVICES
Basically formulation of OR started from USA Army, so it
has wide application in the areas such as:
 Development of New Technology
 Optimization of Cost and Time
 Tender Evaluation
 Setting and Layouts of Defence Projects
 Assessment of “Threat Analysis”
 Strategy of Battle
 Effective Maintenance and Replacement of Equipment
 Inventory Control,
 Transportation
 Supply Depots, etc.

INDUSTRIAL ESTABLISHMENTS
AND PRIVATE SECTOR UNITS
OR can be effectively used in-
Plant Location and Setting Finance Planning
Product and Process Planning
Facility Planning and Construction
Production Planning and Control
Purchasing
Maintenance Management
Personnel Management, etc.

R&D AND ENGINEERING
Research and development being the heart of
technological growth, OR has wide scope and
can be applied in-
Technology Forecasting and Evaluation,
Technology and Project Management,
Preparation of Tender and Negotiation,
Value Engineering,
Work/Method Study and so on.

METHODOLOGIES/APPROACHES
OF OPERATIONAL RESEARCH
1. FORMULATE THE PROBLEM
2. OBSERVE THE SYSTEM/COLLECTION OF DATA
3. FORMULATE A MATHEMATICAL MODEL OF THE
PROBELM
4. VERIFY THE MODEL
5. SOLUTION
6. ANALYSES AND PRESENT THE RESULT
7. IMPLEMENTATION AND EVALUTE RECOMMENDATIONS

TECHNIQUES/TOOLS OF
Linear Programming
Queuing Theory
Transportation Problems
Integer Problems
Assignment Problems
Decision Theory and Games Theory
Replacement Problems
Symbolic Logic

LINEAR PROGRAMMING
 This technique is used to find a solution for optimising a
given objective. Objective may be maximizing profits or
minimizing costs.
 Objective function and Boundary conditions are linear
in nature.
 LPP techniques solve Product-Mix and Distribution
problems of enterprise.
 Its also used to allocate Scarce Resources in optimum
manner in problems of scheduling, product mix, etc.

QUEUING THEORY
 This theory deals with the situations in which queue is
formed, e.g. customers waiting for services, machines
waiting for repairmen, and aircrafts waiting for landing
strips, etc.
 If the Queue will be long the cost will be high due to long
waiting hour.
 This technique is used to analyse the feasibility of adding
facilities and to access the amount and cost of waiting time.
 This calculations can then be used to determine the
desirable number of service facilities.

TRANSPORTATION PROBLEMS
Transportation problems deals with
transportation of a product
 From a number of sources
 With limited supplies
 To number of destinations
 With specified demands
 At the total transportation cost.
The main objective of transportation is to
Schedule Shipment from sources to destinations
in such a way so as to Minimize the Total
Transportation Cost.

INTEGER PROGRAMMING
Integer means complete or whole number. By
using the Integer Programming Algorithm a series
of continuous linear programming problem are
solved in such a way that the solution containing
un-acceptable non-integer value are ruled out and
the best higher programming solution is obtained.

ASSIGNMENT PROBLEMS
It is a special type of linear programming problem. It deals
in allocating the various resources or items to various
activities in a one to one basis in such a way that the time
or cost involved in minimised and the sale or profit is
maximized.
E.g. Manager may like to know which job should be assigned
to which person so that all jobs can be completed in the
shortest possible time.

DECISION THEORY AND
GAME THEORY
Decision Theory is primarily considered with decision
making under the conditions of:
 Risk
 Uncertainity
Game Theory is concerned with:
 Decision Making under Conflict
Hence, both Decision Theory and Game Theory assist the
Decision-Maker in Analysing Problems with numerous
alternative course of action and consequences.

REPLACEMENT PROBLEMS
This Theory is concerned with situations that arise when
some items such as machines, men, etc. require
replacement due to their decreasing efficiency, failure or
break-down.
Sooner or later all the equipments are required to be
replaced because of:
 Obsolescence
 Discovery of New Technology
 Better Design of Equipment
In Replacement Decisions we consider:
 Cost of Equipment to be Installed
 Cost of Equipment Replaced, etc.
Hence, this theory helps to solve all Replacement
Problems.

SYMBOLIC LOGIC
Symbols are more meaningful and accurate. Everything is
Symbolic in this world.
Words, classes of things, functional systems and rules are
substituted with symbols.
The whole problem is converted into algebraic equations
and propositions. Business Problems are not commonly
converted into symbols but calculations are done on
computers, that is why symbols have extensive
applications.

OPERATIONAL RESEARCH AND MANAGEMENT
DECISION-MAKING
 Operation Research increases the creative capabilities
of a decision maker.
 It increases the effectiveness of mgt. decisions.
Management is most of the time making decisions. It is
thus a decision science which helps mgt. to take better
decisions.
 Nowadays, business problems have become so
complex that it is almost impossible for a human being to
comprehend all important factors, OR Techniques can be
helpful in such situations.
 It also helps in ascertaining best locations for factories
and warehouses, project scheduling as well as most
economic means of transportation.
 OR study approach in business decisions leads to better
control, better co-ordination, better system and at the
end better decision.

MODELS & MODELING
 A model in OR is a simplified representation of
an operation, or is a process in which only the
basic aspects or the most important features of a
typical problem under investigation are
considered. The objective of a model is to
identify significant factors and interrelationships.
The reliability of the solution obtained from a
model depends on the validity of the model
representing the real system.

A good model must possess the following
characteristics:
 It should be capable of taking into account, new
formulation without having any changes in its
frame.
 Assumptions made in the model should be as
small as possible.
 Variables used in the model must be less in
number ensuring that it is simple and coherent.
 It should be open to parametric type of
treatment.
 It should not take much time in its construction
for any problem.

Classification of Models
 Based on structure:
A. Iconic or physical models: They are pictorial
representations of real systems and have the
appearance of the real thing.
An iconic model is said to be scaled down or scaled up
according to the dimensions of the model which may be
smaller or greater than that of the real item,
e.g., city maps, houses blueprints, globe, and so on.
These models are easy to observe and describe, but are
difficult to manipulate and are not very useful for the
purpose of prediction

. B. Analog models: These are more abstract than the
iconic ones for there is no look alike correspondence
between these models and real life items. The models in
which one set of properties is used to represent another
set of properties are called analog models.
C. Mathematic / Symbolic models: They are most
abstract in nature. They employ a set of mathematical
symbols to represent the components of the real system.
These variables are related together by means of
mathematical equations to describe the behavior of the
system. The solution of the problem is then obtained by
applying well developed mathematical techniques to the
model.

 Based on function or purpose
A. Descriptive models: A descriptive model simply describes
some aspects of a situation based on observations, survey.
Questionnaire results or other available data. The result of an
opinion poll represents a descriptive model.
B. Predictive models: Such models can answer ‘what if’ type of
questions, i.e. they can make predictions regarding certain events.
For example, based on the survey results, television networks such
models attempt to explain and predict the election results before
all the votes are actually counted.
C. Prescriptive models: Finally, when a predictive model has
been repeatedly successful, it can be used to prescribe a source of
action. For example, linear programming is a prescriptive (or
normative) model because it prescribes what the managers ought
to do.

 Based on certainty
A. Deterministic models: They are those in which
all parameters and functional relationships are
assumed to be known with certainty when the
decision is to be made. Linear programming and
break-even models are the examples of
deterministic models.
B. Probabilistic / Stochastic models: These models
are those in which at least one parameter or
decision variable is a random variable. These
models reflect to some extent the complexity
of the real world and the uncertainty
surrounding it.

 Based on time reference
A. Static models: These models do not consider
the impact of changes that takes place during
the planning horizon, i.e. they are independent
of time. Also, in a static model only one
decision is needed for the duration of a given
time period.
B. Dynamic models: In these models, time is
considered as one of the important variables
and admits the impact of changes generated by
time. Also, in dynamic models, not only one but
a series of interdependent’ decisions is required
during the planning horizon.

 Based on method of solution
A. Analytical models: These models have a specific
mathematical structure-and thus can be solved
by known analytical or mathematical techniques.
For example, a general linear programing model
as well as the specially structured transportation
and assignment models are analytical models. .
B. Simulation models: A simulation model is
essentially computer-assisted experimentation on
a mathematical structure of a real time structure
in order to study the system under a variety of
assumptions.

APPLICATIONS OF OPERATIONS
RESEARCH IN BUSINESS
Accounting:
-Assigning audit teams effectively
- Credit policy analysis
-Cash flow planning
- Developing standard costs
- Establishing costs for byproducts
- Planning of delinquent account strategy
Construction:
-Project scheduling, monitoring and control
- Determination of proper work force
- Deployment of work force
- Allocation of resources to projects

Facilities Planning:
- Factory location and size decision
-Estimation of number of facilities required
-Hospital planning
- International logistic system design
- Transportation loading and unloading
-Warehouse location decision
Finance:
-Building cash management models
- Allocating capital among various alternatives
- Building financial planning models
- Investment analysis
-Portfolio analysis
-Dividend policy making

Manufacturing:
-Inventory control
-Marketing balance projection
- Production scheduling
- Production smoothing
Marketing:
-Advertising budget allocation
-Product introduction timing
-Selection of Product mix
-Deciding most effective packaging alternative
Purchasing:
-Optimal buying
-Optimal reordering
-Materials transfer

Organizational Behavior / Human Resources:
-Personnel planning
-Recruitment of employees
-Skill balancing
-Training program scheduling
-Designing organizational structure more effectively
Research and Development:
- R & D Projects control
- R & D Budget allocation
-Planning of Product introduction

LIMITATIONS OF
Magnitude of Computation
Non-Quantifiable Factors
Distance between User and Analyst
Time and Money Costs
Implementation

MAGNITUDE OF COMPUTATION
Operations research models try to find out optimal
solution taking into account all the factors. But,
these factors are enormous
and,
expressing them in quantity,
and,
establishing relationships among these, Require
voluminous calculations which can be handled only
by computers.

NON-QUANTIFIABLE FACTORS
OR provides solution only when all
elements related to a problem can be
quantified.
All relevant variables do not lend themselves
to quantification. Factors which cannot be
quantified, find no place in OR study. Models
in OR do not take into account qualititative
factors or emotional factors which may be
quite important.

DISTANCE BETWEEN USER
AND ANALYST
OR being specialist’s job requires a
mathematician or statistician, who
might not be aware of the business
problems.
Similarly, a manager fails to understand
the complex working of OR. Thus there
is a gap between the two. Management
itself may offer a lot of resistance due to
conventional thinking.

TIME AND MONEY COST
When basic data are subjected to frequent
changes, incorporating them into the OR models
is a costly proposition.
Moreover, a fairly good solution at present may
be,
More desirable than a perfect OR solution
available after sometime. The computational
time increases depending upon the size of the
problem and accuracy of results desired.

IMPLEMENTATION
Implementation of any decision is a
delicate task. It must take into account the
complexities of human relations and
behaviour. Sometimes, resistance is offered
due to psychological factors which may not
have any bearing on the problem as well as
its solution.

Introduction to Operations Research

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