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Model building in mathematical programming [[electronic resource] /] / H. Paul Williams
Model building in mathematical programming [[electronic resource] /] / H. Paul Williams
Autore Williams H. P
Edizione [5th ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley, 2013
Descrizione fisica 1 online resource (433 p.)
Disciplina 519.7
Soggetto topico Programming (Mathematics)
Mathematical models
Soggetto genere / forma Electronic books.
ISBN 1-299-18870-2
1-118-50618-9
1-118-50617-0
Classificazione 519.7 WIL
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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 objectives3.2.1 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 model3.4.1 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; 3.5.8.3 VARIABLES; 3.5.8.4 OBJECTIVE
3.5.8.5 CONSTRAINTSChapter 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 Advertising5.1.14 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
Record Nr. UNINA-9910463331503321
Williams H. P  
Hoboken, N.J., : Wiley, 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Model building in mathematical programming [[electronic resource] /] / H. Paul Williams
Model building in mathematical programming [[electronic resource] /] / H. Paul Williams
Autore Williams H. P
Edizione [5th ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley, 2013
Descrizione fisica xx, 411 p. : ill
Disciplina 519.7
Soggetto topico Programming (Mathematics)
Mathematical models
ISBN 1-118-50617-0
1-299-18870-2
1-118-50618-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910795968803321
Williams H. P  
Hoboken, N.J., : Wiley, 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Model building in mathematical programming / / H. Paul Williams
Model building in mathematical programming / / H. Paul Williams
Autore Williams H. P
Edizione [5th ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley, 2013
Descrizione fisica xx, 411 p. : ill
Disciplina 519.7
Soggetto topico Mathematical models
Programming (Mathematics)
ISBN 9781118506172
1118506170
9781299188709
1299188702
9781118506189
1118506189
Classificazione 417
519.7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
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.
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.
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.
13.25.1 Indices.
Record Nr. UNINA-9910961737703321
Williams H. P  
Hoboken, N.J., : Wiley, 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui