| Description |
1 online resource (xx, 411 pages) : illustrations |
| Contents |
Machine generated contents note: Part I -- 1. Introduction -- 1.1. concept of a model -- 1.2. Mathematical programming models -- 2. Solving mathematical programming models -- 2.1. Algorithms and packages -- 2.1.1. Reduction -- 2.1.2. Starting solutions -- 2.1.3. Simple bounding constraints -- 2.1.4. Ranged constraints -- 2.1.5. Generalized upper bounding constraints -- 2.1.6. Sensitivity analysis -- 2.2. Practical considerations -- 2.3. Decision support and expert systems -- 2.4. Constraint programming (CP) -- 3. Building linear programming models -- 3.1. importance of linearity -- 3.2. Defining objectives -- 3.2.1. Single objectives -- 3.2.2. Multiple and conflicting objectives -- 3.2.3. Minimax objectives -- 3.2.4. Ratio objectives -- 3.2.5. Non-existent and non-optimizable objectives -- 3.3. Defining constraints -- 3.3.1. Productive capacity constraints -- 3.3.2. Raw material availabilities -- 3.3.3. Marketing demands and limitations -- 3.3.4. Material balance (continuity) constraints -- 3.3.5. Quality stipulations -- 3.3.6. Hard and soft constraints -- 3.3.7. Chance constraints -- 3.3.8. Conflicting constraints -- 3.3.9. Redundant constraints -- 3.3.10. Simple and generalized upper bounds -- 3.3.11. Unusual constraints -- 3.4. How to build a good model -- 3.4.1. Ease of understanding the model -- 3.4.2. Ease of detecting errors in the model -- 3.4.3. Ease of computing the solution -- 3.4.4. Modal formulation -- 3.4.5. Units of measurement -- 3.5. use of modelling languages -- 3.5.1. more natural input format -- 3.5.2. Debugging is made easier -- 3.5.3. Modification is made easier -- 3.5.4. Repetition is automated -- 3.5.5. Special purpose generators using a high level language -- 3.5.6. Matrix block building systems -- 3.5.7. Data structuring systems -- 3.5.8. Mathematical languages -- 3.5.8.1. SETs -- 3.5.8.2. DATA -- 3.5.8.3. VARIABLES -- 3.5.8.4. OBJECTIVE -- 3.5.8.5. CONSTRAINTS -- 4. Structured linear programming models -- 4.1. Multiple plant, product and period models -- 4.2. Stochastic programmes -- 4.3. Decomposing a large model -- 4.3.1. submodels -- 4.3.2. restricted master model -- 5. Applications and special types of mathematical programming model -- 5.1. Typical applications -- 5.1.1. petroleum industry -- 5.1.2. chemical industry -- 5.1.3. Manufacturing industry -- 5.1.4. Transport and distribution -- 5.1.5. Finance -- 5.1.6. Agriculture -- 5.1.7. Health -- 5.1.8. Mining -- 5.1.9. Manpower planning -- 5.1.10. Food -- 5.1.11. Energy -- 5.1.12. Pulp and paper -- 5.1.13. Advertising -- 5.1.14. Defence -- 5.1.15. supply chain -- 5.1.16. Other applications -- 5.2. Economic models -- 5.2.1. static model -- 5.2.2. dynamic model -- 5.2.3. Aggregation -- 5.3. Network models -- 5.3.1. transportation problem -- 5.3.2. assignment problem -- 5.3.3. transhipment problem -- 5.3.4. minimum cost flow problem -- 5.3.5. shortest path problem -- 5.3.6. Maximum flow through a network -- 5.3.7. Critical path analysis -- 5.4. Converting linear programs to networks -- 6. Interpreting and using the solution of a linear programming model -- 6.1. Validating a model -- 6.1.1. Infeasible models -- 6.1.2. Unbounded models -- 6.1.3. Solvable models -- 6.2. Economic interpretations -- 6.2.1. dual model -- 6.2.2. Shadow prices -- 6.2.3. Productive capacity constraints -- 6.2.4. Raw material availabilities -- 6.2.5. Marketing demands and limitations -- 6.2.6. Material balance (continuity) constraints -- 6.2.7. Quality stipulations -- 6.2.8. Reduced costs -- 6.3. Sensitivity analysis and the stability of a model -- 6.3.1. Right-hand side ranges -- 6.3.2. Objective ranges -- 6.3.3. Ranges on interior coefficients -- 6.3.4. Marginal rates of substitution -- 6.3.5. Building stable models -- 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. applicability of integer programming -- 8.2.1. Problems with discrete inputs and outputs -- 8.2.2. Problems with logical conditions -- 8.2.3. Combinatorial problems -- 8.2.4. Non-linear problems -- 8.2.5. Network problems -- 8.3. Solving integer programming models -- 8.3.1. Cutting planes methods -- 8.3.2. Enumerative methods -- 8.3.3. Pseudo-Boolean methods -- 8.3.4. Branch and bound methods -- 9. Building integer programming models I -- 9.1. uses of discrete variables -- 9.1.1. Indivisible (discrete) quantities -- 9.1.2. Decision variables -- 9.1.3. Indicator variables -- 9.2. Logical conditions and 0-1 variables -- 9.3. Special ordered sets of variables -- 9.4. Extra conditions applied to linear programming models -- 9.4.1. Disjunctive constraints -- 9.4.2. Non-convex regions -- 9.4.3. Limiting the number of variables in a solution -- 9.4.4. Sequentially dependent decisions -- 9.4.5. Economies of scale -- 9.4.6. Discrete capacity extensions -- 9.4.7. Maximax objectives -- 9.5. Special kinds of integer programming model -- 9.5.1. Set covering problems -- 9.5.2. Set packing problems -- 9.5.3. Set partitioning problems -- 9.5.4. knapsack problem -- 9.5.5. travelling salesman problem -- 9.5.6. vehicle routing problem -- 9.5.7. quadratic assignment problem -- 9.6. Column generation -- 10. Building integer programming models II -- 10.1. Good and bad formulations -- 10.1.1. number of variables in an IP model -- 10.1.2. number of constraints in an IP model -- 10.2. Simplifying an integer programming model -- 10.2.1. Tightening bounds -- 10.2.2. Simplifying a single integer constraint to another single integer constraint -- 10.2.3. Simplifying a single integer constraint to a collection of integer constraints -- 10.2.4. Simplifying collections of constraints -- 10.2.5. Discontinuous variables -- 10.2.6. alternative formulation for disjunctive constraints -- 10.2.7. Symmetry -- 10.3. Economic information obtainable by integer programming -- 10.4. Sensitivity analysis and the stability of a model -- 10.4.1. Sensitivity analysis and integer programming -- 10.4.2. Building a stable model -- 10.5. When and how to use integer programming -- 11. implementation of a mathematical programming system of planning -- 11.1. Acceptance and implementation -- 11.2. unification of organizational functions -- 11.3. Centralization versus decentralization -- 11.4. collection of data and the maintenance of a model -- Part II -- 12. problems -- 12.1. Food manufacture 1 -- 12.2. Food manufacture 2 -- 12.3. Factory planning 1 -- 12.4. Factory planning 2 -- 12.5. Manpower planning -- 12.5.1. Recruitment -- 12.5.2. Retraining -- 12.5.3. Redundancy -- 12.5.4. Overmanning -- 12.5.5. Short-time working -- 12.6. Refinery optimisation -- 12.6.1. Distillation -- 12.6.2. Reforming -- 12.6.3. Cracking -- 12.6.4. Blending -- 12.7. Mining -- 12.8. Farm planning -- 12.9. Economic planning -- 12.10. Decentralisation -- 12.11. Curve fitting -- 12.12. Logical design -- 12.13. Market sharing -- 12.14. Opencast mining -- 12.15. Tariff rates (power generation) -- 12.16. Hydro power -- 12.17. Three-dimensional noughts and crosses -- 12.18. Optimising a constraint -- 12.19. Distribution 1 -- 12.20. Depot location (distribution 2) -- 12.21. Agricultural pricing -- 12.22. Efficiency analysis -- 12.23. Milk collection -- 12.24. Yield management -- 12.25. Car rental 1 -- 12.26. Car rental 2 -- 12.27. Lost baggage distribution -- 12.28. Protein folding -- 12.29. Protein comparison -- Part III -- 13. Formulation and discussion of problems -- 13.1. Food manufacture 1 -- 13.1.1. single-period problem -- 13.1.2. multi-period problem -- 13.2. Food manufacture 2 -- 13.3. Factory planning 1 -- 13.3.1. single-period problem -- 13.3.2. multi-period problem -- 13.4. Factory planning 2 -- 13.4.1. Extra variables -- 13.4.2. Revised constraints -- 13.5. Manpower planning -- 13.5.1. Variables -- 13.5.2. Constraints -- 13.5.3. Initial conditions -- 13.6. Refinery optimization -- 13.6.1. Variables -- 13.6.2. Constraints -- 13.6.3. Objective -- 13.7. Mining -- 13.7.1. Variables -- 13.7.2. Constraints -- 13.7.3. Objective -- 13.8. Farm planning -- 13.8.1. Variables -- 13.8.2. Constraints -- 13.8.3. Objective function -- 13.9. Economic planning -- 13.9.1. Variables -- 13.9.2. Constraints -- 13.9.3. Objective function -- 13.10. Decentralization -- 13.10.1. Variables -- 13.10.2. Constraints -- 13.10.3. Objective -- 13.11. Curve fitting -- 13.12. Logical design -- 13.13. Market sharing -- 13.14. Opencast mining -- 13.15. Tariff rates (power generation) -- 13.15.1. Variables -- 13.15.2. Constraints -- 13.15.3. Objective function (to be minimized) -- 13.16. Hydro power -- 13.16.1. Variables -- 13.16.2. Constraints -- 13.16.3. Objective function (to be minimized) -- 13.17. Three-dimensional noughts and crosses -- 13.17.1. Variables -- 13.17.2. Constraints -- 13.17.3. Objective -- 13.18. Optimizing a constraint -- 13.19. Distribution 1 -- 13.19.1. Variables -- 13.19.2. Constraints -- 13.19.3. Objectives -- 13.20. Depot location (distribution 2) -- 13.21. Agricultural pricing -- 13.22. Efficiency analysis |
|
Note continued: 13.23. Milk collection -- 13.23.1. Variables -- 13.23.2. Constraints -- 13.23.3. Objective -- 13.24. Yield management -- 13.24.1. Variables -- 13.24.2. Constraints -- 13.24.3. Objective -- 13.25. Car rental 1 -- 13.25.1. Indices -- 13.25.2. Given data -- 13.25.3. Variables -- 13.25.4. Constraints -- 13.25.5. Objective -- 13.26. Car rental 2 -- 13.27. Lost baggage distribution -- 13.27.1. Variables -- 13.27.2. Objective -- 13.27.3. Constraints -- 13.28. Protein folding -- 13.29. Protein comparison -- Part IV -- 14. Solutions to problems -- 14.1. Food manufacture 1 -- 14.2. Food manufacture 2 -- 14.3. Factory planning 1 -- 14.4. Factory planning 2 -- 14.5. Manpower planning -- 14.6. Refinery optimization -- 14.7. Mining -- 14.8. Farm planning -- 14.9. Economic planning -- 14.10. Decentralization -- 14.11. Curve fitting -- 14.12. Logical design -- 14.13. Market sharing -- 14.14. Opencast mining -- 14.15. Tariff rates (power generation) -- 14.16. Hydro power -- 14.17. Three-dimensional noughts and crosses -- 14.18. Optimizing a constraint -- 14.19. Distribution 1 -- 14.20. Depot location (distribution 2) -- 14.21. Agricultural pricing -- 14.22. Efficiency analysis -- 14.23. Milk collection -- 14.24. Yield management -- 14.25. Car rental -- 14.26. Car rental 2 -- 14.27. Lost baggage distribution -- 14.28. Protein folding -- 14.29. Protein comparison |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Copyright © John Wiley & Sons 2013 |
|
Online resource; title from digital title page (viewed March 25, 2013) |
| Subject |
Programming (Mathematics)
|
|
Mathematical models.
|
|
Models, Theoretical
|
|
mathematical models.
|
|
MATHEMATICS -- Linear & Nonlinear Programming.
|
|
Mathematical models
|
|
Programming (Mathematics)
|
| Form |
Electronic book
|
| LC no. |
2012037911 |
| ISBN |
9781118506189 |
|
1118506189 |
|
9781118506172 |
|
1118506170 |
|
1118443330 |
|
9781118443330 |
|
