Operation Research Introduction and Overviews

1. OPERATION RESEARCH

2. Topics
 Quantitative Approach to Decision Making
 History of Operation research
 Overview of Operation Research
 Definition of OR
 OR Models
 Application of OR
 Advantages and Limitations of OR

3. Problem Solving and Decision Making
 Problem solving can be defined as the process of identifying a
difference between the actual and the desired state of affairs and
then taking action to resolve the difference. Problem solving process
consist of seven steps.
1. Identify and define the problem.
2. Determine the set of alternative solutions.
3. Determine the criterion or criteria that will be used to evaluate the alternatives.
4. Evaluate the alternatives.
5. Choose an alternative.
6. Implement the selected alternative.
7. Evaluate the results to determine whether a satisfactory solution has been obtained.

4. Decision Making
 Decision making is the term generally associated with
the first five steps of the problem solving process.
1. Identify and define the problem.
2. Determine the set of alternative solutions.
3. Determine the criterion or criteria that will be used to evaluate
the alternatives.
4. Evaluate the alternatives.
5. Choose an alternative.

5. Example
 You would like a position that will lead to a
satisfying career. Suppose that your job search has
resulted in offers from companies in IBM, TCS, Exide
and Facebook
1. Identify and define the problem.
2. Determine the set of alternative solutions.

6. Step 3: Determine the criteria that will be used to evaluate the alternatives.
 Criteria : Salary Factor (find the best solution with
respect to one criterion are referred to as single-
criterion decision problems.)
Alternatives Salary
IBM 45000
TCS 40000
Exide 48500
Facebook 52000

7. Multi criteria Decision Problems
 Criterion: Salary, Potential for advancement and
job location. What decision you will take?
Alternatives Salary Potential for
Advancement
Job Location
IBM 45000 Average Good
TCS 40000 Excellent Average
Exide 48500 Good Excellent
Facebook 52000 Average Average

8. Decision Making
 Assume we have taken first alternatives as best
decision by some method. (Decision making process
is complete)
 Defined the problem.
 Identified the alternatives.
 Determined the criteria's.
 Evaluated the alternatives.
 Chosen an alternative.

9. Quantitative Analysis and Decision
Making

10. Analyzing the Problem

11. Analyzing the Problem
 Qualitative Analysis : It is based primarily on
manager‟s judgment and experiences. (manager
might faced similar problem in past)
 Quantitative Analysis: By applying management
decision science methodology and analyze the
problem. (some mathematical and statistical tools)

12. Why Quantitative technique
 The problem is complex, and the manager cannot develop a good solution without
the aid of quantitative analysis. ( Ex: Schedule 10,000 workers for 1,00,000
operation)
 The problem is especially important (e.g., a great deal of money is involved), and
the manager desires a thorough analysis before attempting to make a decision.
 The problem is new, and the manager has no previous experience
 The problem is repetitive, and the manager saves time and effort by relying on
quantitative procedures to make routine decision recommendations.

13. History of Operation Research
 Operation research origins in World War II for military
services
 Urgent need to allocate resources at efficient manner.
 British and US called large number of scientists from discipline
were asked to do research on military operation.
 Developed effective method to locate radar (Britain Air
Battle). Developed a better method to manage convoy and
antisubmarine operation(North Atlantic). Developed a method
to utilize resources efficiently( resource cost reduced one half).

14. Development of operation Research
 Success of OR in the war spurred interest in outside
the military (business, industry and government)
 Two factors played a major for rapid growth of OR
 Continuous contribution by scientist's to improve the
techniques of OR
 Computer Revolution

15. Overview of Operation Research
 Define the problem and gather the data
 Formulate a mathematical model to represent the
problem
 Derive a solutions from the model
 Validate the model
 Implement

16. Define the problem
 How to define the problem?
 Study the relevant system (business, industry etc) and
develop a well defined statement of problem to be
considered.
 It helps to determine objectives (Ex: Minimize cost of
operation, maximize the profit of company, maintain high
level of safety) , constraints (limited resources),
interrelationship, possible alternatives, time limits for making
decision and so on.

17. Model
 Models are representations of real objects or situations and
can be presented in various forms. The purpose of any
model is that it enables us to make inferences about the real
situation by studying and analyzing the model
 Iconic model : Physical replica of real objects (airplane, toy truck)
 Mathematical model: Representations of a problem by a system
of symbols and mathematical relationships.
 For example, the total profit from the sale of a product can be
determined by multiplying the profit per unit by the quantity sold.
P= 10X

18. Problem
 How many bowls and mugs should be produced to
maximize profits given labor and materials constraints?
 Product resource requirements and unit profit:
 Total labor hours available is 40 hours and total clay is
120 lb.

19. Mathematical model
Maximize Z = 40X1 + 50X2
subject to:
1X1 + 2X2 ≤40
4X1 + 3X2 ≤ 120
X1, X2 ≥ 0

20. Derive a solution from the model
 Numerous algorithms are available to solve the problem
(ex: simplex algorithm)
 A common theme in OR is search for an optimal or best
solution .
 It also helps to conduct post optimality analysis (what if
analysis: what would happen to optimal solution if different
assumptions are made about future conditions)
 It also helps to identify sensitive parameters of model
(sensitivity analysis)

21. Validate the model
 Model may contains many flaws (missed out some
valuable information while defining the model). So
it won‟t give correct result.
 One way of validating the model is to use a
retrospective test. (Reconstruct the past using
historical data and find shortcomings and require
modifications)

22. Implementation
 Model developer or OR consultant explains about new
system to be adopted (For Ex: Developed a
computerized system for optimally scheduling and
deploying workforce)
 Take frequent feedback and modify the model if
require.
 Document the methodology clearly and accurately
enough so that work is reproducible.

23. Definition of OR
 “Scientific approach to decision making that involves the operations
for organized systems. O.R. is concerned with optimal decision
making in and modelling of deterministic and probabilistic systems
that originate from real life,” – Hillier & Lieberman, Introduction to
Operations Research, 8th Ed., Holden- Day, 2005.
 “Operations Research is the application of scientific methods to
decision problems. It has found wide use and acceptance in all areas
of business, government and industry.” – Saul L. Gass, College of
Business & Management, University of Maryland, 1979.

24. Definition of OR
 “The use of analytic methods adapted from mathematics for solving
operational and business problems” – Computer Dictionary, Charles J.
Sippl and Charles P. Sippl, Howard W. Sams & Co., Inc., Indianapolis,
1978.
 “A scientific method of providing executive department with a
quantitative basis for decisions making operations under their
control.” – Morse & Kimball, Methods of Operations Research,
Columbia University Press for office of Naval Research, 1943 (9th
printing, 1963).

25. OR Models
 Linear Programming:
 It consists of a single objective function, representing either
a profit to be maximized or a cost to be minimized, and a
set of constraints.
 the objective function and constraints are all linear functions.
 Countless real-world applications have been successfully
modeled and solved using linear programming techniques.

26. OR Models
 Network Flow Programming:
 The class of network flow programs includes such problems
as the transportation problem, the assignment problem, the
shortest path problem, the maximum flow problem, the pure
minimum cost flow problem, and the generalized minimum
cost flow problem.
 When a situation can be entirely modeled as a network,
very efficient algorithms exist for the solution of the
optimization problem.

27. OR Models
 Integer Programming:
 Concerned with optimization problems in which some of
the variables are required to take on discrete values.
 Situation like binary decisions such as yes-no, build-no
build or invest-not invest can be modeled easily.

28. OR Models
 Nonlinear Programming:
 When expressions defining the objective function or
constraints of an optimization model are not linear.
 Indeed it can be argued that all linear expressions are
really approximations for nonlinear ones.
 In general a nonlinear programming model is much
more difficult to solve than a similarly sized linear
programming model.

29. OR Models
 Dynamic Programming:
 DP model describes a process in terms of states,
decisions, transitions and returns. The process begins in
some initial state where a decision is made. The
decision causes a transition to a new state.
 The process continues through a sequence of states until
finally a final state is reached. The problem is to find
the sequence that maximizes the total return.

30. OR Models
 Stochastic Programming:
 The mathematical programming models, such as linear
programming, network flow programming and integer
programming generally neglect the effects of uncertainty
and assume that the results of decisions are predictable and
deterministic.
 Stochastic programming explicitly recognizes uncertainty by
using random variables for some aspects of the problem

31. OR Models
 Stochastic Process:
 In many practical situations the attributes of a system
randomly change over time. Examples include the
number of customers in a checkout line, congestion on a
highway, the number of items in a warehouse, and the
price of a financial security, to name a few. When
aspects of the process are governed by probability
theory, we have a stochastic process.

32. OR Models
 Markov Chain:
 the stochastic process can be described by a matrix
which gives the probabilities of moving to each state
from every other state in one time interval.
 It illustrates how to construct a model of this type and
the measures that are available.

33. OR Model
 Game theory:
 The analysis of competitive situations (or situations of
conflict) using mathematical models
 Fundamentally about the study of decision-making
 Investigations are concerned more with choices and
strategies than „best‟ solutions.
It seeks to answer the questions:
 What strategies are there?
 What kinds of solutions are there?

34. Examples of OR in action
 Scheduling: of aircrews and the fleet for airlines, of
vehicles in supply chains, of orders in a factory and of
operating theatres in a hospital.
 Facility planning: computer simulations of airports for
the rapid and safe processing of travelers, improving
appointments systems for medical practice.
 Planning and forecasting: identifying possible future
developments in telecommunications, deciding how much
capacity is needed in a holiday business.

35. Examples of OR in action
 Yield management: setting the prices of airline seats and hotel rooms to
reflect changing demand and the risk of no shows.
 Credit scoring: deciding which customers offer the best prospects for credit
companies.
 Marketing: evaluating the value of sale promotions, developing customer
profiles and computing the life-time value of a customer.
 Defense and peace keeping: finding ways to deploy troops rapidly.

36. Applications of OR
 Yield Management at American Airlines:
 American Airlines estimates the quantifiable benefit of $1.4
billion over a three-year evaluation period and expects an
annual revenue contribution of over $500 million to continue into
the future.
 New Product Market Assessment by Assessor for 450 new
products:
 Assessor has helped reduce the failure rate of new products in
test markets by almost half and saved the 100 client firms an
estimated $120 million.

37. Applications of OR
 Package Routing and Aircraft Scheduling at United Parcel Service :
 planning to buy 30 jets to handle a predicted increase in package
volume. After solving its scheduling problem, UPS determined it could
get by with just 18 to 26 new jets. At $60 million a jet, UPS saved
between $240 and $720 million.
 Interactive Optimization System for GTE Telephone Network
Planning:
 largest local telephone company in the United States. They applied OR
and made a new model which is Netcap. It improved productivity by
more than 500% and saved GTE an estimated $30 million per year in
network construction costs

38. Advantages of OR
 Effective Decisions (Better and quicker decision. helps to evaluate risk and
return of alternatives)
 Better Coordination (OR plays a major role in Overall approach. So it
easily coordinate the decision taken by different department in an
organization)
 Facilitates Control (it helps to find out and correct the deviation in the
performances)
 Improves Productivity (It helps to decide about the selection, location and
size of the factories, warehouses, etc. It helps in inventory control. It helps in
production planning and control. It also helps in manpower planning. It uses
mathematical and statistical techniques to improve overall productivity)

39. Limitations of OR
 In the quantitative analysis of operations research, certain
assumptions and estimates are made for assigning quantitative
values to factors involved. If such estimates are wrong, the result
would be- equally misleading.
 It is not a substitute for the entire process of decision making.
 A knowledge of some concepts of mathematics and statistics is
prerequisite for adoption of quantitative analysis by the managers.
 Intangible factors of human behavior cannot be quantified
accurately and all the patterns of relationships among the factors
may not be covered.