The 5th edition of Model Building in Mathematical Programmingdiscusses the general principles of model building in mathematicalprogramming and demonstrates how they can be applied by usingseveral simplified but practical problems from widely differentcontexts. Suggested formulations and solutions are given togetherwith some computational experience to give the reader a feel forthe computational difficulty of solving that particular type ofmodel. Furthermore, this book illustrates the scope and limitationsof mathematical programming, and shows how it can be applied toreal situations. By emphasizing the importance of the building andinterpreting of models rather than the solution process, the authorattempts to fill a gap left by the many works which concentrate onthe algorithmic side of the subject. In this article, H.P. Williams explains his originalmotivation and objectives in writing the book, how it has beenmodified and updated over the years, what is new in this editionand why it has maintained its relevance and popularity over theyears: http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html
Autorentext
H. Paul Williams, London School of Economics, UK.
Klappentext
Model Building in Mathematical Programming covers a wide range of applications in many diverse areas, such as operational research, systems engineering, agriculture, energy planning, mining, logistics and distribution, computer science, management science, statistics, applied mathematics and mathematical biology.
Model Building in Mathematical Programming aims to provide students with a solid foundation in the principles of model building as well as the more mathematical, algorithmic side of the subject which is conventionally taught. It is also intended to provide managers with a fairly non-technical appreciation of the scope and limitations of mathematical programming.
Praise for the 4th Edition:
"Such a text, and this is the only one of this type I know of, should be the basis of all instruction in Mathematical Programming."
Journal of the Royal Statistical Society
"An excellent introduction ... for students of business administration and people who want to see the utility of operations research."
European Journal of Operational Research
This new edition includes:
- New sections on stochastic programming, column generation and constraint logic programming as well as many enhancements of former sections.
- 29 detailed practical problems, including 5 new problems, to enable the reader to build mathematical programming models using the numerical data.
Zusammenfassung
The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solutions are given together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model. Furthermore, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject.
In this article, H.P. Williams explains his original motivation and objectives in writing the book, how it has been modified and updated over the years, what is new in this edition and why it has maintained its relevance and popularity over the years: http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html
Inhalt
Preface
PART 1
1 Introduction
1.1 The Concept of a Model
1.2 Mathematical Programming Models
2 Solving Mathematical Programming Models
2.1 Algorithms and Packages
2.2 Practical Considerations
2.3 Decision Support and Expert Systems
2.4 Constraint Programming
3 Building Linear Programming Models
3.1 The Importance of Linearity
3.2 Defining Objectives
3.3 Defining Constraints
3.4 How to Build a Good Model
3.5 The Use of Modelling Languages
4 Structured Linear Programming Models
4.1 Multiple Plant, Product, and Period Models
4.2 Stochastic Programming Models
4.3 Decomposing a Large Model
5 Applications and Special Types of Mathematical Programming Model
5.1 Typical Applications
5.2 Economic Models
5.3 Network Models
5.4 Converting Linear Programs to Networks
6 Interpreting and Using the Solution of a Linear Programming Model
6.1 Validating a Model
6.2 Economic Interpretations
6.3 Sensitivity Analysis and the Stability of a Model
6.4 Further Investigations Using a Model
6.5 Presentation of the Solutions
7 Non-linear Models
7.1 Typical Applications
7.2 Local and Global Optima
7.3 Separable Programming
7.4 Converting a Problem to a Separable Model
8 Integer Programming
8.1 Introduction
8.2 The Applicability of Integer Programming
8.3 Solving Integer Programming Models
9 Building Integer Programming Models I
9.1 The Uses of Discrete Variables
9.2 Logical Conditions and Zero-One Variables
9.3 Special Ordered Sets of Variables
9.4 Extra Conditions Applied to Linear Programming Models
9.5 Special Kinds of Integer Programming Model
9.6 Column Generation
10 Building Integer Programming Models II
10.1 Good and Bad Formulations
10.2 Simplifying an Integer Programming Model
10.3 Economic Information Obtainable by Integer Programming
10.4 Sensitivity Analysis and the Stability of a Model
10.5 When and How to Use Integer Programming
11 The Implementation of a Mathematical Programming System of Planning
11.1 Acceptance and Implementation
11.2 The Unification of Organizational Functions
11.3 Centralization versus Decentralization
11.4 The Collection of Data and the Maintenance of a Model
PART 2
12 The Problems
12.1 Food Manufacture 1
When to buy and how to blend
12.2 Food Manufacture 2
Limiting the number of ingredients and adding extra conditions
12.3 Factory Planning 1
What to make, on what machines, and when
12.4 Factory Planning 2
When should machines be down for maintenance
12.5 Manpower Planning
How to recruit, retrain, make redundant, or overman
12.6 Refinery Optimization
How to run an oil refinery
12.7 Mining
Which pits to work and when to close them down
12.8 Farm Planning
How much to grow and rear
12.9 Economic Planning
How should an economy grow
12.10 Decentralization
How to disperse offices from the capital
12.11 Curve Fitting
Fitting a curve to a set of data points
12.12 Logical Design
Constructing an electronic system with a minimum number of components
12.13 Market Sharing
Assigning retailers to company divisions
12.14 Opencast Mining
How much to excavate
12.15 Tariff Rates (Power Generation)
How to determine tariff rates for the sale of electricity
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