SYLLABI
PAPER 6 (ii) : OPERATIONS RESEARCH
UNIT-I
 Operations Research—Meaning, Significance and Scope.
 Introduction to Linear Programming, Formulation of Linear
Programming—Problem,
Graphical
Method,Simplex
Method.Duality in Linear Programming, Definition of Dual
Problem, General Rules in Converting any Primal into its
Dual,
 Transportation problem,
 Assignment problem.
UNIT-II
 Inventory – Types, Nature and Classification,
Economic Lot Size Models, Quality Discounts,
 Basic Concept of Network Models, Preparation of the
Network Diagrams, Project Duration and Critical Path,
probability Statements of Project Durations.
 Games Theory : Two persons zero sum games, Pure
Strategies, Mixed Strategies, Dominance, Introduction
to frequency problems,
 Classification of Sequencing Problems, Processing in
Job through Two Machines.
PRACTICAL WORK :
 One project report in following areas :
Packages in LPP, PERT-CPM in any industry,
Inventory application in any company.
STYLE OF THE PAPER
Section A – Covering Full Syllabus
2 Theory 4 Practical and you have to attempt any 4 of 5 Marks each
Total 20 Marks
Section B– Covering Unit I of the Syllabus
1 Theory 3 Practical and you have to attempt any 2 of 15 Marks each
Total 30 Marks
Section C– Covering Unit II of the Syllabus
1 Theory 3 Practical and you have to attempt any 2 of 15 Marks each
Total 30 Marks
Highest Score You can expect in this Paper 80/80 + 20/20 in
Internals Assessment
SOME FACTS ABOUT MY PAST RESULTS
 More than 75% of my students get more than
75% marks in my subject.
 I find some students who get 100 out of 100
in my subject
 How amongst will achieve this only you will
know but I assure you
 I find some students who get 100 out of 100
in my subject
OPERATIONS RESEARCH : NAMES
Operations Research is also known as:
Decision Science
Management Science
Operations Management
Quantitative Techniques
OPERATIONS RESEARCH: HISTORY
 The roots of OR can be traced back many
decades, when early attempts were made to
use a scientific approach in the management
of organizations.
 However, the beginning of the activity called
operations research has generally been
attributed to the military services early in World
War II.
 Because of the war effort, there was an urgent
need to allocate scarce resources to the
various military operations and to the activities
within each operation in an effective manner.
 Therefore, the British and then the U.S. military
management called upon a large number of
scientists to apply a scientific approach to
dealing with this and other strategic and tactical
problems.
 In effect, they were asked to do research on
(military) operations. These teams of scientists
were the first OR teams.
 By developing effective methods of using the
new tool of radar, these teams were instrumental
in winning the Air Battle of Britain.
 Through their research on how to better manage convoy
and antisubmarine operations, they also played a major
role in winning the Battle of the North Atlantic.
 Similar efforts assisted the Island Campaign in the
Pacific.
 A key person in the post-war development of OR was
George B Dantzig. In 1947, he developed linear
programming and its solution method known as simplex
method.
 Besides linear programming, many other tools of OR
such as statistical control, dynamic programming
queuing theory and inventory theory were well
developed before the end of the 1950s.
 O.R. as a formal subject is about fifty five years
old, origins may be traced to the latter half of
World War II. The impetus for its origin was the
development of radar defense systems for the
Royal Air Force, and the first recorded use of
the term Operations Research is attributed to a
British Air Ministry official named A. P. Rowe
who constituted teams to do “operational
researches” on the communication system and
the control room at a British radar station.
 The studies had to do with improving the operational
efficiency of systems (an objective which is still one of the
cornerstones of modern O.R.). This new approach of picking
an “operational’’ system and conducting “research” on how
to make it run more efficiently soon started to expand into
other arenas of the war.
 Perhaps the most famous of the groups involved in this effort
was the one led by a physicist named P. M. S. Blackett which
included physiologists, mathematicians, astrophysicists, and
even a surveyor. This multifunctional team focus of an
operations research project group is one carried forward to
this day. Blackett’s biggest contribution was in convincing the
authorities of the need for a scientific approach to manage
complex operations, and indeed he is regarded in many
circles as the original operations research analyst.
OPERATIONS RESEARCH : DEFINITIONS
 Operations Research (OR) – The science that
applies mathematical and computer science
tools to support decision making.
 Operations Research is concerned with
scientifically deciding how to best design and
operate
man-machine
systems
usually
requiring the allocating of scarce resources.
-Operations Research Society, America
 OR is the art of winning wars without actually fighting.
-Arthur Clarke
 OR is a scientific method of providing executive
departments with a quantitative basis for decision
regarding the operations under their control.
-Morse and Kimbal
 OR is the art of giving bad answers to problems where
otherwise worse answers are given.
-T.L. Satty
CHARACTERISTICS OF OPERATIONS RESEARCH
OR is a system approach
OR is an Inter-disciplinary team approach.
OR increases creative ability of the decision maker
OR is Scientific approach
 (i) Defining
 (ii) Observing
 (iii) Formulating
 (iv) Testing
 (v) Analyzing
OR is Objectivistic approach
Digital computer
Quantitative solution
OR is a continuing process
Optimizing nature
Human judgment
CHARACTERISTICS OPERATIONS RESEARCH
 Operation Research is the applications of scientific methods,
techniques and tools to problems involving the operations of a
system so as to provide those in control of the system with
optimum solutions to the problems. The significant features of
operation research are as below :
1. OR is a system approach: The essence of systems
approach is to find all significant and indirect effects on all
parts of a system and to evaluate each action in terms of the
effects for the system as a whole. e.g., a new strategy of
marketing department can effect all the other departments of
the organisation and so in evaluating the strategy, not only its
effects on the marketing department should be considered but
also the effects of the proposal on other departments as well.
2.
OR is an Inter-disciplinary team approach: OR
is interdisciplinary in nature and needs a team
approach
solving
economic,
physical,
psychological, biological, sociological and
engineering aspects of any problem by the
assistance of mathematicians statisticians,
engineers, economists, management and
computer experts, this team for a given
problem tries to analyse the cause and effect
relationship between various parameters and
evaluates the outcome of various alternative
strategies.
3.
OR increases creative ability of the decision
maker: OR is a powerful tool in increasing the
effectiveness of managerial decision. OR
techniques help the decision maker to
improve
his
creative
and
judicious
capabilities, analyse and understand the
problem situation leading to better control,
co-ordination, system finally better decisions.
4. OR is Scientific approach : OR gives scientific methods for the
purpose of solving problems, and there is no place of whims a
guesswork in it. It is a formulized process of reasoning and
consists of the following steps:
(i) Defining: The problem to be analyzed clearly and
defining the conditions for observations.
(ii) Observing: Observations are made under different
conditions to determine the behaviour of the system.
(iii) Formulating: A hypothesis describing how the various
factors involved are believed to interact and the best solution
to the problem is formulated on the basis of above
observations.
(iv) Testing: Finally the result of experiment is design and
executed, observations are made and measurements are
recorded.
(v) Analysing: Finally the result of experiment are analysis
and check weather hypothesis is accepted or not. Of the
hypothesis is accepted it means the solution obtained is
optimum.
OR is Objectivistic approach : OR attempts to find out the
strategic or optimal solution to the problem under
consideration. For this purpose, it is required that a measure of
effectiveness be defined which is based on the objectives of
the organisation. This measure is then used as the basis to
compare the alternative courses of action.
5.
6. Digital computer : Use of digital computer has become an
integral part of the operations research approach to decisionmaking. The computer may be required due to the complexity
of the model, volume of data required or the computations to
be made. Many quantitative techniques are available in the
form of ‘canned’ programmes.
7. Quantitative solution. Operation research assists
the management with a quantitative basis for
decision making. OR attempts to provide a
systematic and scientific rational approach for
quantitative solutions to the various managerial
problems.
8. OR is a continuing process : OR is a continuing
process. It continues with the emergence of new
problems, finding and implementing solutions and
interpreting the results of such implementation.
Problems continue to arise in the modern dynamic
environment. As such OR becomes a continuing
process.
9. Optimizing Nature : OR ties to optimize total
return by maximizing the profit and minimizing
the cost or loss.
10. Human judgment : In deriving quantitative
solution, sometimes human factors, play
significant role, in the problems, are ignored.
So, study of the OR is incomplete without a
study of human factors.
OR is Objectivistic approach : OR attempts to find out the
strategic or optimal solution to the problem under
consideration. For this purpose, it is required that a measure of
effectiveness be defined which is based on the objectives of
the organisation. This measure is then used as the basis to
compare the alternative courses of action.
5.
6. Digital computer : Use of digital computer has become an
integral part of the operations research approach to decisionmaking. The computer may be required due to the complexity
of the model, volume of data required or the computations to
be made. Many quantitative techniques are available in the
form of ‘canned’ programmes.
7. Quantitative solution. Operation research assists
the management with a quantitative basis for
decision making. OR attempts to provide a
systematic and scientific rational approach for
quantitative solutions to the various managerial
problems.
8. OR is a continuing process : OR is a continuing
process. It continues with the emergence of new
problems, finding and implementing solutions and
interpreting the results of such implementation.
Problems continue to arise in the modern dynamic
environment. As such OR becomes a continuing
process.
9. Optimizing Nature : OR ties to optimize total
return by maximizing the profit and minimizing
the cost or loss.
10. Human judgment : In deriving quantitative
solution, sometimes human factors, play
significant role, in the problems, are ignored.
So, study of the OR is incomplete without a
study of human factors.
WHY OPERATIONS RESEARCH
 You may ask, “Why must we learn the Operations
Research techniques?” Here are a few motivating
reasons:
 Organizations are becoming more complex, Huge
numbers of choices and relentless time pressures and
margin pressures make the decisions you face more
daunting and more difficult.
 Environments are changing so rapidly that past practices
are no longer adequate. Meanwhile, new enterprise
applications and software are generating massive
amounts of data – and it can see like an overwhelming
task to turn that data into insight and answers.
 The costs of making bad decisions have increased.
OPERATIONS RESEARCH HELPS
 Deciding where to invest capital in order to grow
 Getting more value out of ERP(Enterprise Resource
Planning), CRM (Customer Relationship
Management), and other software systems
 Figuring out the best way to run a call center
 Locating a warehouse or depot to deliver material
s over shorter distances at reduced cost
 Forecasting sales for a new kind of product that has
never marketed before
 Solving complex scheduling problems
 Planning for a potential terrorist attack
 Deciding when to discount, and how much
 Getting more cycles out of manufacturing
equipment
 Optimizing a portfolio of investments, whether it
contains financial securities or pharmaceutical
product inventory
 Deciding how large a budget to devote to Internet
vs. traditional sales
 Planting crops in the face of uncertainty about
weather and consumer demand
SCOPE OF OPERATION RESEARCH
(The Multidisciplinary and Interdisciplinary Nature
of Operations Research)
I. IN DEFENCE OPERATIONS
 Administration
 Intelligence
 Operations, and
 Training and supply.
II.IN INDUSTRY
Applications of operations research in the area of management
1. Production Management : The production manager can
apply OR methods for
 The remunerative policy with regard to time and piece rate.
 Determination of optimum product mix.
 Production, scheduling and sequencing the production run by
allocation of machines.
 Work study operation including time study.
 Selecting plant location and design of the sites.
 Distribution policy
 Loading and unloading facility for road transportation.
 Maintenance crew sizes.
2. MARKETING MANAGEMENT
The marketing manager can apply OR method for
 Product selection, timing and formulation of
competitive strategies.
 Marketing research.
 Distribution strategies.
 Sales forecasting.
 Sales promotion.
 Selection of advertising media and terms of cost
and time factor
 To find optimum number of Salesmen.
3. FINANCIAL MANAGEMENT
The financial manager can apply OR method for
 Apply cash flow analysis for capital budgeting
 Formulate credit policies, evaluate credit risks
 Determine optimum replacement strategies.
 Frame claim and complaint procedures.
 Frame policies regarding capital structure.
 Long range capital requirement.
 Investments portfolio.
 Dividend policies.
4. PERSONAL MANAGEMENT
The personal manager can apply OR method for
 Forecasting the manpower requirement, framing of
recruitment policies, assignment of jobs to machines or
workers etc.
 Selection of suitable personnel with due consideration for
age, education skills training etc.
 Determination of optimum number of persons for each
service centre.
 The promotional policies.
 Mixes of age and skills.
5. PURCHASE DEPARTMENT
The purchased department can apply OR method for
 Determining the quantity and timing of purchase of
raw materials, machinery etc.
 Bidding policies.
 Rules for buying and supplies under varying pries.
 Equipment replacement policies.
 Determination of quantities and timing of purchases.
6. RESEARCH AND DEVELOPMENT DEPARTMENT
The research and development department can
apply OR method for
 Determining the areas for research and
development.
 Scheduling and control of R and D projects.
 Resource allocation and crashing in projects.
 Project selection.
 Reliability and alternative design.
7. MANUFACTURING DEPARTMENT
 The manufacturing department can apply OR
method for :
 Inventory control
 Projection marketing balance.
 Production scheduling
 Production smoothing.
8. ORGANIZATION BEHAVIOUR DEPARTMENT
The OB department can apply OR method
for
Personnel selection and planning.
Scheduling of training programs.
Skills balancing.
Recruitment of Employees.
9. ACCOUNTING DEPARTMENT
The accounting department can apply OR
method for
 Cash flow and fund flow planning.
 Credit policy analysis.
 Planning of delinquent account strategy.
10. TECHNIQUES AND GENERAL MANAGEMENT
The Techniques & General Management can
apply OR method for
 Decision support systems and MIS;
 forecasting.
 Organizational design and control
 Projection management,
 strategic planning.
III. IN GOVERNMENT PLANNING
IV. AGRICULTURE: With the explosion of population and consequent
shortage of food, every country is facing the problem of :
 Optimum allocation of land and various crops in accordance with the
climatic conditions;
 Optimum distribution of water from various resources like canal for
irrigation purposes.
 Thus there is a need of determining best policies under the prescribed
restrictions. Hence a good amount of work can be done in this direction.
V. IN HOSPITALS
VI. IN LIFE INSURANCE CORPORATION
VII. IN CONSTRUCTION PROJECTS
VIII. OPERATIONS RESEARCH MANAGEMENT INFORMATION SYSTEMS
IX. OPERATIONS RESEARCH AS SYSTEM SCIENCE:
The Needs:
Explication, Understanding, Prediction
Observation of the phenomenon
Extensions
Modeling
New Theories
Unification
Using
Existing Models
Constructing
Hypothesis
Obtaining Experimental Data
Testing for Confirmation
Or
Attempt of Refutation
METHODOLOTY OF OR METHODS
Orientation
Problem Definition
Validation and Output Analysis
Solution
Implementation and Monitoring
Data Collection
Model Formulation
Basis of Classification
STRUCTURE
TIME/BEHAVIOUR
Descriptive Normative
Model
Model
Predictive
Model
Static
Symbolic Model
Model
Model
Physical
Model
Iconic
Model
PURPOSE
Analogue
Model
Verbal
Model
Mathematic
Model
DEGREE OF
SOLUTION
CERTAINITY PROCEDURE
Dynamic
Model
Analytical Simulation
Model
Model
Probabilistic Non- Probabilistic
Model
Model
CLASSIFICATION OF OR
MODEL
(A) Classification Based on Structure
. Physical Model : These models provide a physical appearance of the real object
under study either reduced in size or scaled up. These models cannot be
manipulated and not very useful for prediction, therefore, problems such as
portfolio section, media selection, production scheduling, etc. cannot be analysed
with a physical model. Physical models are classified into the following two
categories.
Iconic Models : Iconic models retain some of the physical and characteristics of the
system they represent. An iconic model is either in an idealized form or a scaled
version of the system. It is said to be scaled down when the dimensions of the
model are smaller than those of the real object and model said to be scaled up
when it is bigger than the real object. In other words, it is an image.
Examples :
 A globe representing the earth.
 Blue prints of a home.
 Model of a cell in biology.
 A baby toy car as a model of an automobile.
1
PHYSICAL MODELS
Analogue Model: These models represent a system or object by using set of
properties different from the ones, held by the original object or system.
There is no ‘look-alike’ relation between the model and the original. i.e.
These models represent a system by the set of properties different from that
of the original system and does not resemble physically. After the problem is
solved, the solution is re-interpreted in terms of the original system.
Example :
 Organizational chart represent the state of formal relationships existing between
members of the organization.
 Maps in different colours may represent water, desert, mountains etc.
 Graphs of time series, stock market etc. may be used to represent quantitative
relationship between any two properties.
 Both models are easier to manipulate and can represent dynamic situations; so
analogue model is more popular than iconic models.
SYMBOLIC MODELS
These models use symbols like letters, numbers etc.to represent the
properties of the system. These models are also used to
represent relationships which can be represented in a physical
form. Symbolic models can be classified into two categories:
Verbal Models: These models describe a situation in written or
spoken language.
Example: Written sentences, books, newspapers, journals etc.
Mathematical Models: These models represent the characteristics
of a situation or reality by using a set of mathematical symbols
and relationships. These models are widely used in OR due to
their capacity to depict the complex relationship among the
variables of a problem. Example : ‘+’, ‘–‘, ‘×’, ‘÷’.
CLASSIFICATION BASED ON PURPOSE
The models based on the purpose of their utility include :
Descriptive Models: Descriptive models simply describe some features of a situation based on observation
survey or other available data of a situation and do not predict or recommend.
Example :
 Result of a n opinion poll.
 Block diagram representing an algorithm or method for solving a problem.
Predictive Models: These models indicate that ‘if this occurs then that will follow’. They related dependent
and independent variables and permit trying out, ‘what if’ questions. In other words, these models are
used to predict the outcomes due to a given set of alternatives for the problem.
Example :
 Television network try to predict the election results before the counting of all the votes.
 Rain forecast before actual rainfall.
Normative Models : When a model has been repeatedly successful, it can be used to develop objective
decision rules or criteria for optimal solutions. These models are applicable to repetitive problems.
Example :
 Linear programming is a normative or prescriptive model, because it prescribes what the managers
should do.
CLASSIFICATION BASED ON BEHAVIOUR
Static models : these models are considered independent of time. They
do not take into account the effect of changes taking place during a
particular time period. It involve only one decision for duration of a
given time period.
 Example :an inventory models can be developed and solved to
determine economic order quantity for the next period assuming that
the demand in planning period would remain the same as that for
today.
Dynamic models : these models consider time as one of the important
variables and taken into account the effect of changes generated by
time. This involves not only one, but a series of interdependent
decisions are required.
 Example : dynamic programming in which all possible results are
analyzed and best solution is selected.
CLASSIFICATION BASED ON DEGREE OF
CERTAINTY
Deterministic Models : These models make assumption of certainty
and perfect knowledge. In this model the parameters are
completely defined. Examples: Linear Programming Problems,
Assignment Problems, Transportation Problems , Break even models
etc.
Probabilistic Models : Models in which at least one parameter or
decision variable is a random variable are called probabilistic
models. Variables are independent which is the function of
dependent variable(s). This means payoff due to certain changes
in the independent variable cannot be predicted with certainty.
However, it is possible to predict a pattern of values of both the
variables by their probability distribution. Example : Probabilistic
inventory models are used the conditions of uncertain demand to
decide the economic ordering quantity (EOQ). A game theory
where saddle points or equilibrium points of the player does not
exists, we apply probabilistic model.
CLASSIFICATION BASED ON SOLUTION PROCEDURE
Analytical Models : These models have a specific
mathematical structure and problems can be solved by
running specific solution procedures. Any optimization
model (which requires maximization or minimization of an
objective function) is an analytical model.
 Example :
 A general linear programming problem.
 Special structured transportation and assignment problem.
Simulation Models : These models also have a mathematical
structure but are not solved by applying mathematical
techniques to get a solution. Instead, a simulation model is
essentially a computer assisted experimentation on a
mathematical structure of a real life problem in order to
describe and evaluate its behaviour under certain
assumptions over a period of time.
LIMITATIONS OF OPERATIONS RESEARCH
Operation Research has certain limitations. However, these
limitations are mostly related to the problems of model
building and the time and money factors involved in its
application rather than its practical utility.
Some of them are as follows:
 MAGNITUDE OF COMPUTATIONS
O.R tries to find out optimal solution taking into account all the
factors. In the modern society these factors are enormous
and expressing them in quantity and establishing
relationships among these are required complicated
calculations which can only be handled by machines.
 NON-QUANTIFIABLE FACTORS
O.R provides solution only when all elements related to a
problem can be qualified. All relevant variables do not
lend themselves to quantification. Factors which
cannot be quantified, find no place in O.R.
 GAP BETWEEN MANAGER AND OPERATIONS
RESEARCHER
O.R being specialist’s job requires a mathematician or a
statistician, who might not be aware of the business
problems. Similarly, a manager fails to understand the
complex working of O.R. Management itself may offer
a lot of resistance due to conventional thinking.
 MONEY AND TIME COSTS
When the basic data are subjected to frequent changes,
incorporation them into the O.R models is a costly affair.
Moreover, a fairly good solution at present may be
more desirable than a perfect O.R solution available
after sometime.
 IMPLEMENTATION
Implementation of decisions is a delicate task. It must take
into account the complexities of human relations and
behaviour. Sometimes resistance is offered only due to
psychological factors.

SELECTION OF TECHNIQUE
Operations Research techniques are very useful but they
cannot be used indiscriminately. Choice of technique
depends upon the nature of
problem, operating
conditions,
assumptions,
objectives,
etc.
Thus,
identification and use of an appropriate technique is
essential.
 NOT A SUBSTITUTE OF MANAGEMENT
Operations Research only provides the tools and cannot be
a substitute of management. It only examines the results
of alternative courses of action and final decision is made
by management within its authority and judgment.
 SUB- OPTIMISATION
Sub- optimisation is deciding in respect of a relatively
narrow aspect of the whole business situation or
optimisation of a sub- section of the whole.
Functional heads some times, without taking care of
wider implications, sub- optimise their functions. This
may cause loss in that part of the organisation which
is left out of the exercise and as such should be
avoided.
THANK YOU