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Course
Year
: Deterministic Optimization (D0774)
: 2009
INTRODUCTION MODEL AND MODELING
Meeting 1
Today’s Lecture
• Brief OR
• Optimization
• Model and Modeling
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Operation Research
Optimization
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What is Operations Research?
• Enterprises typically consist of various units whose
operations need to be coordinated
– A typical problem: how to distribute resources across units
so as to maximize efficiency
• OR is the discipline of applying analytical tools based on
mathematical models to help take better decisions in
managing these operations (the “science of better”)
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• Typical decision-making process in OR entails:
1.
2.
3.
4.
Gathering available data
Building an abstract mathematical model
Solving the mathematical problem
Supplying the results to management
Feedback: may
need to enhance
data or model
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A Brief History of OR
• World War II led to the birth of OR
• Scientists and engineers used mathematical tools to
deploy, manage, and analyze military operations, e.g.,
– deployment of the radar
– management of convoy and submarine operations
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Perhaps the single
most important
catalyst in the
advancement of
OR
• Many important developments took place in this period.
Most notably George Dantzig invented the simplex
method for solving linear programs (LPs) in 1947
– One of the first applications was the diet problem:
given foods with varying nutrient amounts, plan a diet that
satisfies the desired nutrient requirements + the foodamount constraints, and minimizes cost
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After the War:
• Industrial boom led to rapid increase in size of
corporations – growing need for systematic decisionmaking tools
• Managers began to realize both, the modeling power of
LPs and OR tools, and their potency in improving
efficiency even under existing technology; applications
increased manifold
• Serendipitously, great advances were made in
computational technology, which allowed one to solve
problems of ever-increasing size via OR tools
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Where is OR Today?
• Immense computing power available readily and fairly
cheaply, e.g., PCs
• A half-century of research in OR has led to:
– very good theoretical understanding
– various software packages, e.g., CPLEX, LINDO,
XPRESS-MP, being available that can be used “off-the
shelf”
• OR is everywhere – from booking an airline ticket, to
checking into your hotel
• By the end of this course, you will be able to solve realworld problems on your PC using these OR tools!
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What you will learn ?
• Mathematical Modeling
– learn a variety of ways of modeling real-world problems as
structured mathematical problems
• Solution Methods
– learn to use powerful optimization tools to solve the problems
arising in your mathematical models
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Introduction OR
• Winston: “a scientific approach to decision
making, which seeks to determine how best to
design and operate a system, usually under
conditions requiring the allocation of scarce
resources.”
• Kimball & Morse: “a scientific method of
providing executive departments with a
quantitative basis for decisions regarding the
operations under their control.”
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• Provides rational basis for decision making
– Solves the type of complex problems that turn up in
the modern business environment
– Builds mathematical and computer models of
organizational systems composed of people,
machines, and procedures
– Uses analytical and numerical techniques to make
predictions and decisions based on these models
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• Draws upon
– engineering, management, mathematics
• Closely related to the "decision sciences"
– applied mathematics, computer science, economics,
industrial engineering and systems engineering
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Methodology of Operations Research*
The Seven Steps to a Good OR Analysis
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Defining Model
• Need to develop a clear and concise statement
that gives direction and meaning to the following
steps
• This may be the most important and difficult step
• It is essential to go beyond symptoms and identify true
causes
• May be necessary to concentrate on only a few of the
problems – selecting the right problems is very
important
• Specific and measurable objectives may have to be
developed
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Developing Model
$ Sales
• Quantitative analysis models are realistic,
solvable, and understandable mathematical
representations of a situation
$ Advertising
There are different types of models
Scale
models
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Schematic
models
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• Models generally contain variables (controllable
and uncontrollable) and parameters
• Controllable variables are generally the decision
variables and are generally unknown
• Parameters are known quantities that are a part
of the problem
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