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Model Building in Mathematical Programming, 5th Edition

Book Description

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.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
    1. Preface to the Fifth Edition
  6. Part I
    1. Chapter 1: Introduction
      1. 1.1 The concept of a model
      2. 1.2 Mathematical programming models
    2. Chapter 2: Solving mathematical programming models
      1. 2.1 Algorithms and packages
      2. 2.2 Practical considerations
      3. 2.3 Decision support and expert systems
      4. 2.4 Constraint programming (CP)
    3. Chapter 3: Building linear programming models
      1. 3.1 The importance of linearity
      2. 3.2 Defining objectives
      3. 3.3 Defining constraints
      4. 3.4 How to build a good model
      5. 3.5 The use of modelling languages
    4. Chapter 4: Structured linear programming models
      1. 4.1 Multiple plant, product and period models
      2. 4.2 Stochastic programmes
      3. 4.3 Decomposing a large model
    5. Chapter 5: Applications and special types of mathematical programming model
      1. 5.1 Typical applications
      2. 5.2 Economic models
      3. 5.3 Network models
      4. 5.4 Converting linear programs to networks
    6. Chapter 6: Interpreting and using the solution of a linear programming model
      1. 6.1 Validating a model
      2. 6.2 Economic interpretations
      3. 6.3 Sensitivity analysis and the stability of a model
      4. 6.4 Further investigations using a model
      5. 6.5 Presentation of the solutions
    7. Chapter 7: Non-linear models
      1. 7.1 Typical applications
      2. 7.2 Local and global optima
      3. 7.3 Separable programming
      4. 7.4 Converting a problem to a separable model
    8. Chapter 8: Integer programming
      1. 8.1 Introduction
      2. 8.2 The applicability of integer programming
      3. 8.3 Solving integer programming models
    9. Chapter 9: Building integer programming models I
      1. 9.1 The uses of discrete variables
      2. 9.2 Logical conditions and 0–1 variables
      3. 9.3 Special ordered sets of variables
      4. 9.4 Extra conditions applied to linear programming models
      5. 9.5 Special kinds of integer programming model
      6. 9.6 Column generation
    10. Chapter 10: Building integer programming models II
      1. 10.1 Good and bad formulations
      2. 10.2 Simplifying an integer programming model
      3. 10.3 Economic information obtainable by integer programming
      4. 10.4 Sensitivity analysis and the stability of a model
      5. 10.5 When and how to use integer programming
    11. Chapter 11: The implementation of a mathematical programming system of planning
      1. 11.1 Acceptance and implementation
      2. 11.2 The unification of organizational functions
      3. 11.3 Centralization versus decentralization
      4. 11.4 The collection of data and the maintenance of a model
  7. Part II
    1. Chapter 12: The problems
      1. 12.1 Food manufacture 1
      2. 12.2 Food manufacture 2
      3. 12.3 Factory planning 1
      4. 12.4 Factory planning 2
      5. 12.5 Manpower planning
      6. 12.6 Refinery optimisation
      7. 12.7 Mining
      8. 12.8 Farm planning
      9. 12.9 Economic planning
      10. 12.10 Decentralisation
      11. 12.11 Curve fitting
      12. 12.12 Logical design
      13. 12.13 Market sharing
      14. 12.14 Opencast mining
      15. 12.15 Tariff rates (power generation)
      16. 12.16 Hydro power
      17. 12.17 Three-dimensional noughts and crosses
      18. 12.18 Optimising a constraint
      19. 12.19 Distribution 1
      20. 12.20 Depot location (distribution 2)
      21. 12.21 Agricultural pricing
      22. 12.22 Efficiency analysis
      23. 12.23 Milk collection
      24. 12.24 Yield management
      25. 12.25 Car rental 1
      26. 12.26 Car rental 2
      27. 12.27 Lost baggage distribution
      28. 12.28 Protein folding
      29. 12.29 Protein comparison
  8. Part III
    1. Chapter 13: Formulation and discussion of problems
      1. 13.1 Food manufacture 1
      2. 13.2 Food manufacture 2
      3. 13.3 Factory planning 1
      4. 13.4 Factory planning 2
      5. 13.5 Manpower planning
      6. 13.6 Refinery optimization
      7. 13.7 Mining
      8. 13.8 Farm planning
      9. 13.9 Economic planning
      10. 13.10 Decentralization
      11. 13.11 Curve fitting
      12. 13.12 Logical design
      13. 13.13 Market sharing
      14. 13.14 Opencast mining
      15. 13.15 Tariff rates (power generation)
      16. 13.16 Hydro power
      17. 13.17 Three-dimensional noughts and crosses
      18. 13.18 Optimizing a constraint
      19. 13.19 Distribution 1
      20. 13.20 Depot location (distribution 2)
      21. 13.21 Agricultural pricing
      22. 13.22 Efficiency analysis
      23. 13.23 Milk collection
      24. 13.24 Yield management
      25. 13.25 Car rental 1
      26. 13.26 Car rental 2
      27. 13.27 Lost baggage distribution
      28. 13.28 Protein folding
      29. 13.29 Protein comparison
  9. Part IV
    1. Chapter 14: Solutions to problems
      1. 14.1 Food manufacture 1
      2. 14.2 Food manufacture 2
      3. 14.3 Factory planning 1
      4. 14.4 Factory planning 2
      5. 14.5 Manpower planning
      6. 14.6 Refinery optimization
      7. 14.7 Mining
      8. 14.8 Farm planning
      9. 14.9 Economic planning
      10. 14.10 Decentralization
      11. 14.11 Curve fitting
      12. 14.12 Logical design
      13. 14.13 Market sharing
      14. 14.14 Opencast mining
      15. 14.15 Tariff rates (power generation)
      16. 14.16 Hydro power
      17. 14.17 Three-dimensional noughts and crosses
      18. 14.18 Optimizing a constraint
      19. 14.19 Distribution 1
      20. 14.20 Depot location (distribution 2)
      21. 14.21 Agricultural pricing
      22. 14.22 Efficiency analysis
      23. 14.23 Milk collection
      24. 14.24 Yield management
      25. 14.25 Car rental
      26. 14.26 Car rental 2
      27. 14.27 Lost baggage distribution
      28. 14.28 Protein folding
      29. 14.29 Protein comparison
  10. References
  11. Author Index
  12. Subject Index