Operations
Research
(OR)
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Chapter One
Introduction to OR
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Chapter objectives
After completing this unit, you will be able to:
• Discuss Meaning and definition of
OR
• Understand the history of OR
• Explain Features of OR
• Discuss Significance of operations
research.
• Discuss OR techniques
• Explain Quantitative Analysis and
Decision Making
• Models and Model Building
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Introduction - Terminology
European- Operational Research
The Americans- Operations Research; shorten OR
An other term MS, IE, DS, Problem Solving
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History of OR
• War Baby
• Started in Great Britain during WWII (1939-1945)
• Failure of missions were very high.
• scientists and technocrats formed a team to study the problems arising out of
different situations.
• 1940s: the term of OR get more prominence when research was carried out on
the design and analysis of mathematical models for military operations.
Contd…
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 Till 1950s OR confined to military operations,
 1950: OR began to develop in Industrial fields in USA.
 1951: the first book of Morse and Kimball “Methods of Operations
Research” published.
 1952: the Operations Research Society of America came into being.
 1957: IFORS established at Oxford
 Since then the OR/MS/DS has become more applicable in all
management aspects of a system, product and service.
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What is OR?
Operations
 The activities carried out in an organization/elsewhere.
Research
 The process of observation and testing characterized by the scientific method.
Situation, problem statement, model construction, validation, experimentation,
candidate solutions.
Model
 An abstract representation of reality. Mathematical, physical, narrative, set of
rules in computer program.
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Meaning and Definition of OR
 OR is the application of a scientific approach to solving management
problems
Bernard W. Taylor III
 OR is the application of scientific methods by inter-disciplinary teams to
solve problems involving the control of organized (man-machine systems) so
as to provide solutions which best serve the purposes of the organization as a
whole
Ackoff and Sasieni 1968
Cont’d
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 OR is concerned with scientifically deciding how to best design and operate man-
machine system usually requiring the allocation of scare resources.”
Operations Research Society, America
 OR is a scientific approach to problem solving for executive management
Harvey Wagner
 OR is the art of winning wars without fighting
Clarke
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Basic OR concepts
 OR is the representation of real-world system by mathematical models with
a view to optimizing
 Mathematical model consists
 Decision variable –unknowns
 Constraints- physical limitation of the system
 An objective function
 An optimal solution
 OR is application of scientific methods/thinking in decision making
 Decision have to be made
 Using quantitative (explicit, articulated) approach –better decision than
qualitative approach
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FEATURES OF OR
(i) Decision-making
(ii) Scientific Approach
(iii) Inter-disciplinary Team Approach
(iv) System Approach
(v) Use of models and computers
(vi) Require willing executives
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Application Areas of Operations Research
There are so many application areas of operations research; to mention some of the
most widely known areas:
• Forecasting
• Maintenance and Repair
• Production Scheduling
• Accounting procedures
• Inventory Control
•
• Capital Budgeting
• Natural Resource Management
• Transportation
• Research and Development
• Plant location
• Health Care
• Human Resource Management
• Quality Control
• Advertising and sales research
• Equipment Replacement, etc.
Packaging
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Significance of Operations Research
 The main purpose of O.R. is to provide a rational basis for decisions
making in the absence of complete information
 Enables proper deployment of resources
• Helps in minimizing waiting and servicing costs
• Enables the management to decide when to buy and how much to buy
• Assists in choosing an optimum strategy
• Renders great help in optimum resource allocation
• Facilitates the process of decision making
• Helps a lot in the preparation of future managers
 Optimizing plant revenues
 Improving the efficiency of a production line
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Techniques of OR
2. Inventory models
3. Replacement models
The commonly used techniques include
4. Network models
1. Allocation models :
5. Waiting- line models(Queuing theory)
Linear programming
6. Simulation
Non-linear programming
7. Sequencing models
Transportation models
Assignment models
8. Decision theory
9. Game theory
Integer programming
Goal programming
Dynamic programming
10. Markov models
11. Regression and correlation
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Quantitative Analysis & the Decision Making Process
 In order to understand the role of quantitative analysis in managerial type of
problems, it is better to have a look at the decision making process.
Decision Making: is the process of selecting a feasible course of action from a set
of alternative, so as to solve problems.
 The decision making process is initiated by a problem.
 The intention of the manager, when making a decision, is to solve that problem.
 In doing so, the manager first makes an analysis of the alternatives.
 There are two forms of analysis— qualitative and quantitative.
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The Management science process
Observation
Problem definition
Model construction
Feedback
Solution
Implementation
Management
science
techniques
Steps in the management science process
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 Observation - Identification of a problem that exists (or may occur
soon) in a system or organization.
 Definition of the Problem - problem must be clearly and consistently
defined, showing its boundaries and interactions with the objectives of the
organization.
 Model Construction - Development of the functional mathematical
relationships that describe the decision variables, objective function and
constraints of the problem.
 Model Solution - Models solved using management science techniques.
 Model Implementation - Actual use of the model or its solution.
Decision Making Process
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Qualitative analysis
based upon managerial
experience and judgment
Summary &
evaluation
Managerial
Problem
Quantitative analysis based
upon mathematical
techniques
Figure 1.1 The Decision Making Process
Decision
Cont…
 In qualitative analysis, intuition and the manager’s subjective judgment and
experience are used.
 This type of problem solving is more an art than a science.
The qualitative approach is usually used when:
 The problem is simple
 The problem is familiar
 The costs involved are not so great
 Immediate decisions are needed
Cont…
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The quantitative approach is used when:
 The problem is complex
 The problem is unacquainted
 The costs involved are substantial
 Enough time is available to analyze the problem
Cont….
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 Both the quantitative and qualitative analyses of a problem provide important
information for the decision maker.
 quantitative analysis tend to be more objective than those based on a purely
qualitative analysis.
 For this reason OR makes use of quantitative models.
Steps of decision making
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1. Identify and define the problem;
2. Determine the set of alternative solutions;
3. Determine the criteria to evaluate alternatives;
4. Analyze the alternatives;
5. Select the best alternative/make the decision;
6. Implementing the solution;
7. Establishing a control, follow up and evaluation system;
Models and model building
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 Model is a theoretical abstraction(approximation) of a real-life problem.
 In OR, the problem is expressed in the form of a model.
 A management science model is an abstract representation of an
existing problem situation.
 It can be in the form of a graph or chart, but most frequently a
management science model consists of a set of mathematical
relationships.
Cont…..
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There are certain significant advantages gained when using a model.
 Problem`s under consideration become controllable through a model
 It provides a logical and systematic approach to the problem
 It provides the limitations and scope of an activity
 It helps to eliminate duplications
 It helps in finding solutions for research and improvements in a system.
Problem Solving Process
Goal:
• Solve a problem
• Model must be valid
• Model must be tractable
• Solution must be useful
Formulate the
Problem
Situation
Problem
Statement
Implement a Solution
Data
Construct
a Model
Problem Definition
Implement
the Solution
Model
Model Construction
Procedure
Find
a Solution
Analysis (Model Solution)
Establish
a Procedure
Implementation & Follow-up
Test the Model
and the Solution
Solution
Tools
Figure 1.2 The management science approach
Relationship between the Manager and O.R. Specialist
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The key responsibility of manager is decision making. The role of the O.R.
specialist is to help the manager make better decisions.
 Recognize from organizational symptoms that a problem exists.
 Manager
 Decide what variables are involved; state the problem
 Both
 Investigating methods to solve the problem
 OR specialist
 Test alternative solutions
 OR specialist
 Determine which solution is most effective
 Both
 Choose the solution to be used
 Manager
 Put the solution into action
 both
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Classification of Models
 The classification of models is a subjective problem. They may be
distinguished as follows:
 Models by function
 Models by degree of abstraction
 Models by structure
 Models by nature of an environment
 Models by the extent of generality
1. Models based on Function/purpose:
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A. Descriptive Models: uses surveys , questionnaire, inference of observations to
describe the situation.
Ex. Plant Layout diagram, Block diagram of an algorithm.
B. Predictive Models: These models are the results of query: “ What will follow if
this occurs or does not occur?”.
Ex. Preventive Maintenance Trouble Shooting chart or procedures.
C. Normative or Optimization Models: designed to provide optimal solution to the
problem subject to a certain limitations or constraints on use of resources.
Ex. LP Problem
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2. Models based on Structure and Abstraction :
A. Iconic or Physical Models (It is also called Static Model): are pictorial representations of real systems
 These models are easy to observe and describe but are difficult to manipulate.
E.g. the structure of an atom, layout drawing of factory, model of an airplane etc.
B. Analog Models:
 They are more abstract than iconic models.
 These models are less specific, less concrete but easier to manipulate than iconic models.
 Abstract models mostly showing inter and intra relationships between two or more parameters.
For example It may show the relationship between an input with that of an output.
For instance; histogram, frequency table, cause-effect diagram, flow charts, Gantt charts etc.
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Cont…..
C. Mathematical or Symbolic Models:
 They are most abstract in nature.
 Here, a set of relations is represented in the form of mathematical equations
 Its function is more explanatory than descriptive.
Example:
1. (x + y) 2 = x2+2xy+y2
2. Max. Z=3000x1 +2500x2
Subject to:
2x1+x2 < 40
x1+3x2 < 45
x1< 12
x1 ,
x2 > 0
x1 and x2 are decision variables.
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3. Models based on certainty/ Nature of an Environment :
(1) Deterministic Models: all the parameters of decision variables are constants
and their functional relationship are known with certainty.
Eg. LP, Integer programming etc.
(2) Probabilistic or Stochastic Models: This is the model in which at least one
of the decision variable or parameter is random in nature.
Eg. Queuing theory, decision analysis etc.
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4. Models by Extent of Generality
 These models can be categorized in to:
A. Specific Models: when a model presents a system at some specific time
B. General Models: are models applicable to all situations without time
bound. Simulation and Heuristic models fall under this category.
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Limitations of OR
• The inherent limitations concerning mathematical expressions
• High costs are involved in the use of OR techniques
• OR does not take into consideration the intangible factors
• OR is only a tool of analysis and not the complete decision-making process
• Other limitations
 Bias
 Internal resistance
 Competence
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