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Preface <p>PART 1</p> <p>1 Introduction</p> <p>1.1 The Concept of a Model</p> <p>1.2 Mathematical Programming Models</p> <p>2 Solving Mathematical Programming Models</p> <p>2.1 Algorithms and Packages</p> <p>2.2 Practical Considerations</p> <p>2.3 Decision Support and Expert Systems</p> <p>2.4 Constraint Programming </p> <p>3 Building Linear Programming Models</p> <p>3.1 The Importance of Linearity</p> <p>3.2 Defining Objectives</p> <p>3.3 Defining Constraints</p> <p>3.4 How to Build a Good Model</p> <p>3.5 The Use of Modelling Languages</p> <p>4 Structured Linear Programming Models</p> <p>4.1 Multiple Plant, Product, and Period Models</p> <p>4.2 Stochastic Programming Models</p> <p>4.3 Decomposing a Large Model</p> <p>5 Applications and Special Types of Mathematical Programming Model</p> <p>5.1 Typical Applications</p> <p>5.2 Economic Models</p> <p>5.3 Network Models</p> <p>5.4 Converting Linear Programs to Networks</p> <p>6 Interpreting and Using the Solution of a Linear Programming Model</p> <p>6.1 Validating a Model</p> <p>6.2 Economic Interpretations</p> <p>6.3 Sensitivity Analysis and the Stability of a Model</p> <p>6.4 Further Investigations Using a Model</p> <p>6.5 Presentation of the Solutions</p> <p>7 Non-linear Models</p> <p>7.1 Typical Applications</p> <p>7.2 Local and Global Optima</p> <p>7.3 Separable Programming</p> <p>7.4 Converting a Problem to a Separable Model</p> <p>8 Integer Programming</p> <p>8.1 Introduction</p> <p>8.2 The Applicability of Integer Programming</p> <p>8.3 Solving Integer Programming Models</p> <p>9 Building Integer Programming Models I</p> <p>9.1 The Uses of Discrete Variables</p> <p>9.2 Logical Conditions and Zero—One Variables</p> <p>9.3 Special Ordered Sets of Variables</p> <p>9.4 Extra Conditions Applied to Linear Programming Models</p> <p>9.5 Special Kinds of Integer Programming Model</p> <p>9.6 Column Generation</p> <p>10 Building Integer Programming Models II</p> <p>10.1 Good and Bad Formulations</p> <p>10.2 Simplifying an Integer Programming Model</p> <p>10.3 Economic Information Obtainable by Integer Programming</p> <p>10.4 Sensitivity Analysis and the Stability of a Model</p> <p>10.5 When and How to Use Integer Programming</p> <p>11 The Implementation of a Mathematical Programming System of Planning</p> <p>11.1 Acceptance and Implementation</p> <p>11.2 The Unification of Organizational Functions</p> <p>11.3 Centralization versus Decentralization</p> <p>11.4 The Collection of Data and the Maintenance of a Model</p> <p>PART 2</p> <p>12 The Problems</p> <p>12.1 Food Manufacture 1</p> <p>When to buy and how to blend</p> <p>12.2 Food Manufacture 2</p> <p>Limiting the number of ingredients and adding extra conditions</p> <p>12.3 Factory Planning 1</p> <p>What to make, on what machines, and when</p> <p>12.4 Factory Planning 2</p> <p>When should machines be down for maintenance</p> <p>12.5 Manpower Planning</p> <p>How to recruit, retrain, make redundant, or overman</p> <p>12.6 Refinery Optimization</p> <p>How to run an oil refinery</p> <p>12.7 Mining</p> <p>Which pits to work and when to close them down</p> <p>12.8 Farm Planning</p> <p>How much to grow and rear</p> <p>12.9 Economic Planning</p> <p>How should an economy grow</p> <p>12.10 Decentralization</p> <p>How to disperse offices from the capital</p> <p>12.11 Curve Fitting</p> <p>Fitting a curve to a set of data points</p> <p>12.12 Logical Design</p> <p>Constructing an electronic system with a minimum number of components</p> <p>12.13 Market Sharing</p> <p>Assigning retailers to company divisions</p> <p>12.14 Opencast Mining</p> <p>How much to excavate</p> <p>12.15 Tariff Rates (Power Generation)</p> <p>How to determine tariff rates for the sale of electricity</p> <p>12.16 Hydro Power</p> <p>How to generate and combine hydro and thermal electricity generation</p> <p>12.17 Three-dimensional Noughts and Crosses</p> <p>A combinatorial problem</p> <p>12.18 Optimizing a Constraint</p> <p>Reconstructing an integer programming constraint more simply</p> <p>12.19 Distribution 1</p> <p>Which factories and depots to supply which customers</p> <p>12.20 Depot Location (Distribution 2)</p> <p>Where should new depots be built</p> <p>12.21 Agricultural Pricing</p> <p>What prices to charge for dairy products</p> <p>12.22 Efficiency Analysis</p> <p>How to use data envelopment analysis to compare efficiencies of garages</p> <p>12.23 Milk Collection</p> <p>How to route and assign milk collection lorries to farms</p> <p>12.24 Yield Management</p> <p>What quantities of airline tickets to sell at what prices and what times</p> <p>12.25 Car Rental 1</p> <p>How many cars to own and where to locate them</p> <p>12.26 Car Rental 2</p> <p>Where should repair capacity be increased</p> <p>12.27 Lost Baggage Distribution</p> <p>Which vehicles should go to which customers and in what order</p> <p>12.28 Protein Folding</p> <p>How a string of Amino Acids is likely to fold</p> <p>12.29 Protein Comparison</p> <p>How similar are two proteins</p> <p>PART 3</p> <p>13 Formulation and Discussion of Problems</p> <p>13.1 Food Manufacture 1</p> <p>13.2 Food Manufacture 2</p> <p>13.3 Factory Planning 1</p> <p>13.4 Factory Planning 2</p> <p>13.5 Manpower Planning</p> <p>13.6 Refinery Optimization</p> <p>13.7 Mining</p> <p>13.8 Farm Planning</p> <p>13.9 Economic Planning</p> <p>13.10 Decentralization</p> <p>13.11 Curve Fitting</p> <p>13.12 Logical Design</p> <p>13.13 Market Sharing</p> <p>13.14 Opencast Mining</p> <p>13.15 Tariff Rates (Power Generation)</p> <p>13.16 Hydro Power</p> <p>13.17 Three-dimensional Noughts and Crosses</p> <p>13.18 Optimizing a Constraint</p> <p>13.19 Distribution 1</p> <p>13.20 Depot Location (Distribution 2)</p> <p>13.21 Agricultural Pricing</p> <p>13.22 Efficiency Analysis</p> <p>13.23 Milk Collection</p> <p>13.24 Yield Management</p> <p>13.25 Car Rental 1</p> <p>13.26 Car Rental 2</p> <p>13.27 Lost Baggage Distribution</p> <p>13.28 Protein Folding</p> <p>13.29 Protein Comparison</p> <p>PART 4</p> <p>14 Solutions to Problems</p> <p>14.1 Food Manufacture 1</p> <p>14.2 Food Manufacture 2</p> <p>14.3 Factory Planning 1</p> <p>14.4 Factory Planning 2</p> <p>14.5 Manpower Planning</p> <p>14.6 Refinery Optimization</p> <p>14.7 Mining</p> <p>14.8 Farm Planning</p> <p>14.9 Economic Planning</p> <p>14.10 Decentralization</p> <p>14.11 Curve Fitting</p> <p>14.12 Logical Design</p> <p>14.13 Market Sharing</p> <p>14.14 Opencast Mining</p> <p>14.15 Tariff Rates (Power Generation)</p> <p>14.16 Hydro Power</p> <p>14.17 Three-dimensional Noughts and Crosses</p> <p>14.18 Optimizing a Constraint</p> <p>14.19 Distribution 1</p> <p>14.20 Depot Location (Distribution 2)</p> <p>14.21 Agricultural Pricing</p> <p>14.22 Efficiency Analysis</p> <p>14.23 Milk Collection</p> <p>14.24 Yield Management</p> <p>14.25 Car Rental 1</p> <p>14.26 Car Rental 2</p> <p>14.27 Lost Baggage Distribution</p> <p>14.28 Protein Folding</p> <p>14.29 Protein Comparison</p> <p>References</p> <p>Author Index</p> <p>Subject Index</p>

<p><b>H. Paul Williams</b>, London School of Economics, UK.</p>

<p><i>Model Building in Mathematical Programming</i> 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.</p> <p><i>Model Building in Mathematical Programming</i> 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.</p> <p><b>Praise for the <i>4th Edition</i>:</b></p> <p>"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."<br /><i>Journal of the Royal Statistical Society</i></p> <p>"An excellent introduction ... for students of business administration and people who want to see the utility of operations research."<br /><i>European Journal of Operational Research</i></p> <p><b>This new edition includes:</b></p> <ul> <li>New sections on stochastic programming, column generation and constraint logic programming as well as many enhancements of former sections.</li> <li>29 detailed practical problems, including 5 new problems, to enable the reader to build mathematical programming models using the numerical data.</li> </ul>

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