Model building in mathematical programming
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 solution...
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Chichester [England]
Wiley
2013
John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydání: | 5th ed |
| Témata: | |
| ISBN: | 9781118443330, 1118443330, 9781118506172, 1118506170 |
| On-line přístup: | Získat plný text |
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| Abstract | 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 [http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html] |
|---|---|
| AbstractList | 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 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 [http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html] 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. |
| Author | H. Paul Williams |
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| Edition | 5th ed 5 1 Fifth edition. 5th Edition |
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| Notes | Includes bibliographical references and indexes |
| OCLC | 810039791 842860131 |
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| PublicationDate | 2013/01/01 2013 2013-01-18 |
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| PublicationDecade | 2010 |
| PublicationPlace | Chichester [England] |
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| Publisher | Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
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| Snippet | The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates... |
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| SubjectTerms | BUSINESS & ECONOMICS Mathematical models Programming (Mathematics) |
| TableOfContents | 12.27 Lost baggage distribution -- 12.28 Protein folding -- 12.29 Protein comparison -- Part III -- Chapter 13 Formulation and discussion of problems -- 13.1 Food manufacture 1 -- 13.1.1 The single-period problem -- 13.1.2 The multi-period problem -- 13.2 Food manufacture 2 -- 13.3 Factory planning 1 -- 13.3.1 The single-period problem -- 13.3.2 The 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 -- 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 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 An 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 -- Chapter 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 II -- Chapter 12 The 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 3.5.8.3 VARIABLES -- 3.5.8.4 OBJECTIVE -- 3.5.8.5 CONSTRAINTS -- Chapter 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 The submodels -- 4.3.2 The restricted master model -- Chapter 5 Applications and special types of mathematical programming model -- 5.1 Typical applications -- 5.1.1 The petroleum industry -- 5.1.2 The 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 The supply chain -- 5.1.16 Other applications -- 5.2 Economic models -- 5.2.1 The static model -- 5.2.2 The dynamic model -- 5.2.3 Aggregation -- 5.3 Network models -- 5.3.1 The transportation problem -- 5.3.2 The assignment problem -- 5.3.3 The transhipment problem -- 5.3.4 The minimum cost flow problem -- 5.3.5 The shortest path problem -- 5.3.6 Maximum flow through a network -- 5.3.7 Critical path analysis -- 5.4 Converting linear programs to networks -- Chapter 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 The 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 -- Chapter 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 -- Chapter 8 Integer programming -- 8.1 Introduction -- 8.2 The 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 -- Chapter 9 Building integer programming models I -- 9.1 The 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 The knapsack problem -- 9.5.5 The travelling salesman problem -- 9.5.6 The vehicle routing problem -- 9.5.7 The quadratic assignment problem -- 9.6 Column generation -- Chapter 10 Building integer programming models II -- 10.1 Good and bad formulations -- 10.1.1 The number of variables in an IP model -- 10.1.2 The number of constraints in an IP model -- 10.2 Simplifying an integer programming model Cover -- Title Page -- Copyright -- Contents -- Preface -- Part I -- Chapter 1 Introduction -- 1.1 The concept of a model -- 1.2 Mathematical programming models -- Chapter 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) -- Chapter 3 Building linear programming models -- 3.1 The 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 The use of modelling languages -- 3.5.1 A 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 13.25.1 Indices 13.16 Hydro power -- 13.17 Three-dimensional noughts and crosses -- 13.18 Optimizing a constraint -- 13.19 Distribution 1 -- 13.20 Depot location (distribution 2) -- 13.21 Agricultural pricing -- 13.22 Efficiency analysis -- 13.23 Milk collection -- 13.24 Yield management -- 13.25 Car rental 1 -- 13.26 Car rental 2 -- 13.27 Lost baggage distribution -- 13.28 Protein folding -- 13.29 Protein comparison -- Part IV -- Chapter 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 -- References -- Author Index -- Subject Index Intro -- Title Page -- Copyright -- Dedication -- Preface -- Preface to the Fifth Edition -- Part I -- Chapter 1: Introduction -- 1.1 The concept of a model -- 1.2 Mathematical programming models -- Chapter 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 (CP) -- Chapter 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 -- Chapter 4: Structured linear programming models -- 4.1 Multiple plant, product and period models -- 4.2 Stochastic programmes -- 4.3 Decomposing a large model -- Chapter 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 -- Chapter 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 -- Chapter 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 -- Chapter 8: Integer programming -- 8.1 Introduction -- 8.2 The applicability of integer programming -- 8.3 Solving integer programming models -- Chapter 9: Building integer programming models I -- 9.1 The uses of discrete 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 -- 9.5 Special kinds of integer programming model -- 9.6 Column generation Chapter 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 -- Chapter 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 II -- Chapter 12: The 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 -- 12.6 Refinery optimisation -- 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 -- Chapter 13: Formulation and discussion of problems -- 13.1 Food manufacture 1 -- 13.2 Food manufacture 2 -- 13.3 Factory planning 1 -- 13.4 Factory planning 2 -- 13.5 Manpower planning -- 13.6 Refinery optimization -- 13.7 Mining -- 13.8 Farm planning -- 13.9 Economic planning -- 13.10 Decentralization -- 13.11 Curve fitting -- 13.12 Logical design -- 13.13 Market sharing -- 13.14 Opencast mining -- 13.15 Tariff rates (power generation) |
| Title | Model building in mathematical programming |
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