Operation Research

1. INTRODUCTION
TO
OPERATION RESEARCH

2. 2
Introduction
• Operations Research is an Art and Science
• It had its early roots in World War II and is
flourishing in business and industry with the
aid of computer
• Primary applications areas of Operations
Research include forecasting, production
scheduling, inventory control, capital
budgeting, and transportation.

3. INTRODUCTION TO
OPERATIONAL RESEARCH
Operational Research is a systematic and
analytical approach to decision making and
problem solving.
Operational Research is an Branch of
applied mathematics that uses techniques
and statistics to arrive at Optimal solutions to
solve complex problems.

4. • 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 PROFESSION.

5. 5
What is Operations Research?
Operations
The activities carried out in an organization.
Research
The process of observation and testing characterized
by the scientific method. Situation, problem
statement, model construction, validation,
experimentation, candidate solutions.
Operations Research is a quantitative approach to
decision making based on the scientific method of
problem solving.

6. 6
What is Operations Research?
• Operations Research is the scientific
approach to execute decision making, which
consists of:
– The art of mathematical modeling of
complex situations
– The science of the development of solution
techniques used to solve these models
– The ability to effectively communicate the
results to the decision maker

7. 7
What Do they do
1. OR professionals aim to provide rational bases for
decision making by seeking to understand and
structure complex situations and to use this
understanding to predict system behavior and
improve system performance.
2. Much of this work is done using analytical and
numerical techniques to develop and manipulate
mathematical and computer models of
organizational systems composed of people,
machines, and procedures.

8. HISTORY OF
OPERATIONAL RESEARCH
• 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 say 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.

9.  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.
HISTORY OF
OPERATIONAL RESEARCH

10. 1890
Frederick Taylor
Scientific
Management
[Industrial
Engineering]
1900
•Henry Gannt
[Project Scheduling]
•Andrey A. Markov
[Markov Processes]
•Assignment
[Networks]
1910
•F. W. Harris
[Inventory Theory]
•E. K. Erlang
[Queuing Theory]
1920
•William Shewart
[Control Charts]
•H.Dodge – H.Roming
[Quality Theory]
1930
Jon Von Neuman –
Oscar Morgenstern
[Game Theory]
1940
•World War 2
•George Dantzig
[Linear
Programming]
•First Computer
1950
•H.Kuhn - A.Tucker
[Non-Linear Prog.]
•Ralph Gomory
[Integer Prog.]
•PERT/CPM
•Richard Bellman
[Dynamic Prog.]
ORSA and TIMS
1960
•John D.C. Litle
[Queuing Theory]
•Simscript - GPSS
[Simulation]
1970
•Microcomputer
1980
•H. Karmarkar
[Linear Prog.]
•Personal computer
•OR/MS Softwares
1990
•Spreadsheet
Packages
•INFORMS

11. Definition
• OR is the application of the methods of science to
complex problems in the direction and management of
large system of men, machines, materials and money in
industry, business, government and defense.
• The distinctive approach is to develop a scientific model
of the system incorporating measurements of factors
such as chance and risk, with which to predict and
compare the outcomes of alternative decisions,
strategies or controls. The purpose is to help
management in determining its policy & actions
scientifically
-- Operation Research Society - UK

12. • OR is concerned with scientifically deciding
how to best design and operate man-machine
systems usually requiring the allocation of
scarce resources.
-- Operation Research Society, America

13. FEATURES OF
OPERATIONAL RESEARCH
Decision-Making
Scientific Approach
Inter-Disciplinary Team Approach
System Approach
Objectives

14. 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.

15. 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.

16. 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.

17. 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.

18. OBJECTIVE
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.

19. SCOPE OF
OPERATIONAL RESEARCH
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 given
in next slide.

20. FIELDS
National Planning and Budgeting
Defence Services
Industrial Establishment and Private Sector
Units
R & D and Engineering

21. PHASES IN OR
• JUDGEMENT PHASE.
• RESEARCH PHASE.
• ACTION PHASE.

22. JUDGEMENT PHASE
• Identification of real-life problem.
• Selection of an appropriate objective & the values of
various variable related to this objective
• Application of the appropriate scale of measurement
• Formulation of appropriate model of the problem,
abstracting the essential information to obtain the
decision’s makers goals.

23. RESEARCH PHASE
• Observation & data collection for better
understanding of the problem
• Formulation of hypothesis and model
• Experimentation to test the hypothesis on basis of
additional data.
• Analysis of the available information & verification of
the hypothesis using pre-established measure of
desirability
• Prediction of various result from the hypothesis
• Generalization of the result & consideration of
alternative methods.

24. ACTION PHASE
• Making recommendation for implementing
the decision by an individual who is an the
position to implement result

25. Deterministic Models Stochastic Models
• Linear Programming • Discrete-Time Markov Chains
• Network Optimization • Continuous-Time Markov Chains
• Integer Programming • Queuing
• Nonlinear Programming • Decision Analysis
Operations Research Models

26. Deterministic models assume all data are known
with certainty
Deterministic models involve optimization
Stochastic models explicitly represent uncertain
data via random variables or stochastic processes
Stochastic models characterize / estimate system
performance.
Deterministic vs. Stochastic Models

27. Problem Solving and Decision Making
• 7 Steps of Problem Solving
(First 5 steps are the process of decision making)
– Identify and define the problem.
– Determine the set of alternative solutions.
– Determine the criteria for evaluating the alternatives.
– Evaluate the alternatives.
– Choose an alternative.
---------------------------------------------------------------
– Implement the chosen alternative.
– Evaluate the results.

28. Quantitative Analysis and Decision
Making
• Potential Reasons for a Quantitative Analysis
Approach to Decision Making
– The problem is complex.
– The problem is very important.
– The problem is new.
– The problem is repetitive.

29. Problem Solving Process
Data
Solution
Find
a Solution
Tools
Situation
Formulate the
Problem
Problem
Statement
Test the Model
and the Solution
Procedure
Establish
a Procedure
Implement
the Solution
Construct
a Model
Model
Implement a Solution
Goal: solve a problem
• Model must be valid
• Model must be
tractable
• Solution must be
useful

30. The Situation
• May involve current operations or proposed
developments due to expected market shifts
• May become apparent through consumer
complaints or through employee
suggestions
• May be a conscious effort to improve
efficiency or respond to an unexpected crisis
Example: Internal nursing staff not happy with their schedules; hospital using
too many external nurses.
Data
Situation

31. Problem Formulation
• Define variables
• Define constraints
• Identify data requirements
Example: Maximize individual nurse preferences subject to demand
requirements, or minimize nurse dissatisfaction costs.
Formulate the
Problem
Problem
Statement
Data
Situation
• Describe system
• Define boundaries
• State assumptions
• Select performance measures

32. Constructing a Model
• Problem must be translated
from verbal, qualitative terms to
logical, quantitative terms
• A logical model is a series of
rules, usually embodied in a
computer program
Example: Define relationships between individual nurse assignments
and preference violations; define tradeoffs between the use
of internal and external nursing resources.
Construct
a Model
Model
Formulate the
Problem
Problem
statement
Data
Situation
• A mathematical model is a collection of
functional relationships by which allowable
actions are delimited and evaluated.

33. Model Development
• Models are representations of real objects
or situations.
• Three forms of models are iconic, analog,
and mathematical.
– Iconic models are physical replicas (scalar
representations) of real objects.
– Analog models are physical in form, but do not
physically resemble the object being modeled.

34. – Mathematical models represent real world
problems through a system of mathematical
formulas and expressions based on key
assumptions, estimates, or statistical analyses.

35. 35
Advantages of Models
• Generally, experimenting with models
(compared to experimenting with the real
situation):
– requires less time
– is less expensive
– involves less risk

36. Mathematical Models
• Cost/benefit considerations must be made in
selecting an appropriate mathematical
model.
• Frequently a less complicated (and perhaps
less precise) model is more appropriate than
a more complex and accurate one due to cost
and ease of solution considerations.

37. Mathematical Models
• Relate decision variables (controllable inputs) with
fixed or variable parameters (uncontrollable inputs).
• Frequently seek to maximize or minimize some
objective function subject to constraints.
• Are said to be stochastic if any of the uncontrollable
inputs (parameters) is subject to variation (random),
otherwise are said to be deterministic.
• Generally, stochastic models are more difficult to
analyze.
• The values of the decision variables that provide the
mathematically-best output are referred to as the
optimal solution for the model.

38. 38
Transforming Model Inputs into
Output
Uncontrollable Inputs
(Environmental Factors)
Controllable
Inputs
(Decision Variables)
Output
(Projected Results)
Mathematical
Model

39. Solving the Mathematical Model
• Many tools are available as
discussed in this course
• Some lead to “optimal”
solutions
• Others only evaluate
candidates  trial and
error to find “best” course
of action
Example: Collect input data -- nurse profiles and demand requirements; apply
algorithm; post-process results to get monthly schedules.
Model
Solution
Find a
solution
Tools

40. Model Solution
• Involves identifying the values of the decision variables
that provide the “best” output for the model.
• One approach is trial-and-error.
– might not provide the best solution
– inefficient (numerous calculations required)
• Special solution procedures have been developed for
specific mathematical models.
– some small models/problems can be solved by hand
calculations
– most practical applications require using a computer

41. Computer Software
• A variety of software packages are available
for solving mathematical models, some are:
– Spreadsheet packages such as Microsoft Excel
– The Management Scientist (MS)
– Quantitative system for business (QSB)
– LINDO, LINGO
– Quantitative models (QM)
– Decision Science (DS)

42. Model Testing and Validation
• Often, the goodness/accuracy of a model cannot be assessed
until solutions are generated.
• Small test problems having known, or at least expected,
solutions can be used for model testing and validation.
• If the model generates expected solutions:
– use the model on the full-scale problem.
• If inaccuracies or potential shortcomings inherent in the
model are identified, take corrective action such as:
– collection of more-accurate input data
– modification of the model

43. Implementation
• A solution to a problem usually implies
changes for some individuals in the
organization
• Often there is resistance to change,
making the implementation difficult
• A user-friendly system is needed
• Those affected should go through
training
Situation
Procedure
Implement
the Procedure
Example: Implement nurse scheduling system in one unit at a time. Integrate
with existing HR and T&A systems. Provide training sessions during
the workday.

44. Implementation and Follow-Up
• Successful implementation of model results is
of critical importance.
• Secure as much user involvement as possible
throughout the modeling process.
• Continue to monitor the contribution of the
model.
• It might be necessary to refine or expand the
model.

45. Report Generation
• A managerial report, based on the results of
the model, should be prepared.
• The report should be easily understood by the
decision maker.
• The report should include:
– the recommended decision
– other pertinent information about the results (for
example, how sensitive the model solution is to the
assumptions and data used in the model)

46. Examples of OR Applications
• Rescheduling aircraft in response to groundings and
delays
• Planning production for printed circuit board
assembly
• Scheduling equipment operators in mail processing
& distribution centers
• Developing routes for propane delivery
• Adjusting nurse schedules in light of daily
fluctuations in demand

47. Advantages
• Structured approach to problems.
• Critical approach to problem solving.

48. Shortcomings
• Solutions are derived by making simplified
assumptions so the solutions have limitations.
• Sometime Models do not represent the realistic
situations in which decisions must be made.
• Decision maker is not fully aware of the limitations of
the model.
• Many real world problems just cannot have an OR
solution.

49. Opportunities
• It compels the decision maker to quite explicit
about the objective, assumption and his
perspective to the constraints.
• Variables which influence decisions are
considered.
• Gaps in data required to support solutions to a
problem.
• Management of time because models can be
solved by a computer.

50. Application OR
• Finance & Accounting
• Marketing
• Purchasing, procurement and Exploration
• Production Management
• Manufacturing
• Maintenance and Project scheduling
• Personnel Management
• MIS & General Management
• Government.

51. Application Areas
• Strategic planning
• Supply chain management
• Pricing and revenue management
• Logistics and site location
• Optimization
• Marketing research

52. Applications Areas (cont.)
• Scheduling
• Portfolio management
• Inventory analysis
• Forecasting
• Sales analysis
• Auctioning
• Risk analysis