Model building in mathematical programming:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, N.J.
Wiley
2013
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| Ausgabe: | fifth edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xx, 411 Seiten Illustrationen, Diagramme |
| ISBN: | 9781118443330 |
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Datensatz im Suchindex
| _version_ | 1804150060354633728 |
|---|---|
| adam_text | Titel: Model building in mathematical programming
Autor: Williams, Hilary P
Jahr: 2013
Model Building in Mathematical Programming Fifth Edition H. Paul Williams London School of Economics, UK ©WILEY A John Wiley Sons. Ltd.. Publication
Contents Preface xvii Part I 1 1 Introduction 3 1.1 The concept of a model 3 1.2 Mathematical programming models 5 2 Solving mathematical programming models 11 2.1 Algorithms and packages 11 2.1.1 Reduction 12 2.1.2 Starting solutions 12 2.1.3 Simple bounding constraints 12 2.1.4 Ranged constraints 13 2.1.5 Generalized upper bounding constraints 13 2.1.6 Sensitivity analysis 13 2.2 Practical considerations 13 2.3 Decision support and expert systems 16 2.4 Constraint programming (CP) 17 3 Building linear programming models 21 3.1 The importance of linearity 21 3.2 Defining objectives 23 3.2.1 Single objectives 24 3.2.2 Multiple and conflicting objectives 26 3.2.3 Minimax objectives 27 3.2.4 Ratio objectives 28 3.2.5 Non-existent and non-optimizable objectives 29 3.3 Defining constraints 29 3.3.1 Productive capacity constraints 29 3.3.2 Raw material availabilities 30 3.3.3 Marketing demands and limitations 30 3.3.4 Material balance (continuity) constraints 30
CONTENTS 3.3.5 Quality stipulations 31 3.3.6 Hard and soft constraints 31 3.3.7 Chance constraints 32 3.3.8 Conflicting constraints 32 3.3.9 Redundant constraints 34 3.3.10 Simple and generalized upper bounds 35 3.3.11 Unusual constraints 35 3.4 How to build a good model 36 3.4.1 Ease of understanding the model 36 3.4.2 Ease of detecting errors in the model 37 3.4.3 Ease of computing the solution 37 3.4.4 Modal formulation 38 3.4.5 Units of measurement 40 3.5 The use of modelling languages 40 3.5.1 A more natural input format 41 3.5.2 Debugging is made easier 41 3.5.3 Modification is made easier 41 3.5.4 Repetition is automated 41 3.5.5 Special purpose generators using a high level language 41 3.5.6 Matrix block building systems 42 3.5.7 Data structuring systems 42 3.5.8 Mathematical languages 42 3.5.8.1 SETs 43 3.5.8.2 DATA 43 3.5.8.3 VARIABLES 43 3.5.8.4 OBJECTIVE 43 3.5.8.5 CONSTRAINTS 43 Structured linear programming models 45 4.1 Multiple plant, product and period models 45 4.2 Stochastic programmes 53 4.3 Decomposing a large model 55 4.3.1 The submodels 63 4.3.2 The restricted master model 64 Applications and special types of mathematical programming model 67 5.1 Typical applications 67 5.1.1 The petroleum industry 68 5.1.2 The chemical industry 68 5.1.3 Manufacturing industry 68 5.1.4 Transport and distribution 69 5.1.5 Finance 69 5.1.6 Agriculture 70
CONTENTS ix 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 6 Interpreting and using the solution of a linear programming model 103 6.1 Validating a model 103 6.1.1 Infeasible models 103 6.1.2 Unbounded models 104 6.1.3 Solvable models 105 6.2 Economic interpretations 107 6.2.1 The dual model 109 6.2.2 Shadow prices 112 6.2.3 Productive capacity constraints 114 6.2.4 Raw material availabilities 114 6.2.5 Marketing demands and limitations 114 6.2.6 Material balance (continuity) constraints 114 6.2.7 Quality stipulations 114 6.2.8 Reduced costs 116 6.3 Sensitivity analysis and the stability of a model 121 6.3.1 Right-hand side ranges 121 6.3.2 Objective ranges 125 6.3.3 Ranges on interior coefficients 128 6.3.4 Marginal rates of substitution 131 6.3.5 Building stable models 132 70 70 71 71 71 72 72 72 72 73 74 74 80 81 81 82 87 88 89 93 93 94 98
133 135 137 137 140 147 153 155 155 156 156 158 158 160 161 162 162 163 163 164 165 165 165 165 166 172 177 182 183 184 186 186 187 188 188 189 189 191 193 195 195 198 CONTENTS 6.4 Further investigations using a model 6.5 Presentation of the solutions 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 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 Building integer programming models I 9.1 The uses of discrete variables 9.2 9.3 9.4 9.5 9.1.1 Indivisible (discrete) quantities 9.1.2 Decision variables 9.1.3 Indicator variables Logical conditions and 0-1 variables Special ordered sets of variables 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 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
CONTENTS xi 9.5.7 The quadratic assignment problem 199 9.6 Column generation 201 10 Building integer programming models II 207 10.1 Good and bad formulations 207 10.1.1 The number of variables in an IP model 207 10.1.2 The number of constraints in an IP model 211 10.2 Simplifying an integer programming model 218 10.2.1 Tightening bounds 218 10.2.2 Simplifying a single integer constraint to another single integer constraint 220 10.2.3 Simplifying a single integer constraint to a collection of integer constraints 222 10.2.4 Simplifying collections of constraints 226 10.2.5 Discontinuous variables 228 10.2.6 An alternative formulation for disjunctive constraints 229 10.2.7 Symmetry 230 10.3 Economic information obtainable by integer programming 231 10.4 Sensitivity analysis and the stability of a model 238 10.4.1 Sensitivity analysis and integer programming 238 10.4.2 Building a stable model 239 10.5 When and how to use integer programming 240 11 The implementation of a mathematical programming system of planning 243 11.1 Acceptance and implementation 243 11.2 The unification of organizational functions 245 11.3 Centralization versus decentralization 247 11.4 The collection of data and the maintenance of a model 249 Part II 251 12 The problems 253 12.1 Food manufacture 1 253 12.2 Food manufacture 2 255 12.3 Factory planning 1 255 12.4 Factory planning 2 256 12.5 Manpower planning 256 12.5.1 Recruitment 257 12.5.2 Retraining 257 12.5.3 Redundancy 258 12.5.4 Overmanning 258 12.5.5 Short-time working 258
xii CONTENTS 12.6 Refinery optimisation 258 12.6.1 Distillation 258 12.6.2 Reforming 259 12.6.3 Cracking 259 12.6.4 Blending 260 12.7 Mining 261 12.8 Farm planning 262 12.9 Economic planning 263 12.10 Decentralisation 265 12.11 Curve fitting 266 12.12 Logical design 266 12.13 Market sharing 267 12.14 Opencast mining 269 12.15 Tariff rates (power generation) 270 12.16 Hydro power 271 12.17 Three-dimensional noughts and crosses 272 12.18 Optimising a constraint 273 12.19 Distribution 1 273 12.20 Depot location (distribution 2) 275 12.21 Agricultural pricing 276 12.22 Efficiency analysis 278 12.23 Milk collection 278 12.24 Yield management 282 12.25 Car rental 1 284 12.26 Car rental 2 287 12.27 Lost baggage distribution 287 12.28 Protein folding 289 12.29 Protein comparison 290 Part III 293 13 Formulation and discussion of problems 295 13.1 Food manufacture 1 296 13.1.1 The single-period problem 296 13.1.2 The multi-period problem 297 13.2 Food manufacture 2 299 13.3 Factory planning 1 300 13.3.1 The single-period problem 300 13.3.2 The multi-period problem 301 13.4 Factory planning 2 302 13.4.1 Extra variables 302 13.4.2 Revised constraints 303 13.5 Manpower planning 303 13.5.1 Variables 304
CONTENTS xiii 13.5.2 Constraints 305 13.5.3 Initial conditions 305 13.6 Refinery optimization 306 13.6.1 Variables 307 13.6.2 Constraints 308 13.6.3 Objective 310 13.7 Mining 310 13.7.1 Variables 310 13.7.2 Constraints 311 13.7.3 Objective 312 13.8 Farm planning 312 13.8.1 Variables 312 13.8.2 Constraints 313 13.8.3 Objective function 315 13.9 Economic planning 316 13.9.1 Variables 316 13.9.2 Constraints 316 13.9.3 Objective function 317 13.10 Decentralization 317 13.10.1 Variables 318 13.10.2 Constraints 318 13.10.3 Objective 319 13.11 Curve fitting 319 13.12 Logical design 320 13.13 Market sharing 322 13.14 Opencast mining 324 13.15 Tariff rates (power generation) 325 13.15.1 Variables 325 13.15.2 Constraints 325 13.15.3 Objective function (to be minimized) 326 13.16 Hydropower 326 13.16.1 Variables 326 13.16.2 Constraints 326 13.16.3 Objective function (to be minimized) 327 13.17 Three-dimensional noughts and crosses 327 13.17.1 Variables 327 13.17.2 Constraints 328 13.17.3 Objective 328 13.18 Optimizing a constraint 328 13.19 Distribution 1 330 13.19.1 Variables 331 13.19.2 Constraints 331 13.19.3 Objectives 332 13.20 Depot location (distribution 2) 332 13.21 Agricultural pricing 333
XIV CONTENTS 13.22 Efficiency analysis 335 13.23 Milk collection 336 13.23.1 Variables 336 13.23.2 Constraints 336 13.23.3 Objective 337 13.24 Yield management 337 13.24.1 Variables 338 13.24.2 Constraints 338 13.24.3 Objective 340 13.25 Car rental 1 340 13.25.1 Indices 340 13.25.2 Given data 340 13.25.3 Variables 341 13.25.4 Constraints 341 13.25.5 Objective 342 13.26 Car rental 2 342 13.27 Lost baggage distribution 343 13.27.1 Variables 343 13.27.2 Objective 344 13.27.3 Constraints 344 13.28 Protein folding 344 13.29 Protein comparison 345 Part IV 347 14 Solutions to problems 349 14.1 Food manufacture 1 349 14.2 Food manufacture 2 349 14.3 Factory planning 1 350 14.4 Factory planning 2 351 14.5 Manpower planning 354 14.6 Refinery optimization 356 14.7 Mining 357 14.8 Farm planning 358 14.9 Economic planning 359 14.10 Decentralization 361 14.11 Curve fitting 361 14.12 Logical design 363 14.13 Market sharing 363 14.14 Opencast mining 364 14.15 Tariff rates (power generation) 364 14.16 Hydro power 366 14.17 Three-dimensional noughts and crosses 368 14.18 Optimizing a constraint 369
CONTENTS xv 14.19 Distribution 1 369 14.20 Depot location (distribution 2) 371 14.21 Agricultural pricing 371 14.22 Efficiency analysis 372 14.23 Milk collection 374 14.24 Yield management 376 14.25 Car rental 379 14.26 Car rental 2 380 14.27 Lost baggage distribution 380 14.28 Protein folding 382 14.29 Protein comparison 382 References 383 Author index 397 Subject index 401
|
| any_adam_object | 1 |
| author | Williams, Hilary P. 1943- |
| author_GND | (DE-588)135946328 |
| author_facet | Williams, Hilary P. 1943- |
| author_role | aut |
| author_sort | Williams, Hilary P. 1943- |
| author_variant | h p w hp hpw |
| building | Verbundindex |
| bvnumber | BV040740325 |
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| dewey-full | 519.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7 |
| dewey-search | 519.7 |
| dewey-sort | 3519.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | fifth edition |
| format | Book |
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| id | DE-604.BV040740325 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:32:55Z |
| institution | BVB |
| isbn | 9781118443330 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025720276 |
| oclc_num | 835294650 |
| open_access_boolean | |
| owner | DE-634 DE-29T DE-706 DE-384 DE-91 DE-BY-TUM DE-521 DE-526 DE-91S DE-BY-TUM DE-83 |
| owner_facet | DE-634 DE-29T DE-706 DE-384 DE-91 DE-BY-TUM DE-521 DE-526 DE-91S DE-BY-TUM DE-83 |
| physical | xx, 411 Seiten Illustrationen, Diagramme |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Wiley |
| record_format | marc |
| spelling | Williams, Hilary P. 1943- (DE-588)135946328 aut Model building in mathematical programming H. Paul Williams ; London school of economics, UK fifth edition Hoboken, N.J. Wiley 2013 xx, 411 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Programming (Mathematics) Mathematical models Mathematisches Modell Modellierung (DE-588)4170297-9 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Modell (DE-588)4039798-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Methode (DE-588)4038971-6 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Modell (DE-588)4039798-1 s 1\p DE-604 Optimierung (DE-588)4043664-0 s 2\p DE-604 Anwendung (DE-588)4196864-5 s 3\p DE-604 Methode (DE-588)4038971-6 s 4\p DE-604 Modellierung (DE-588)4170297-9 s 5\p DE-604 Erscheint auch als Online-Ausgabe 978-1-118-50618-9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025720276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Williams, Hilary P. 1943- Model building in mathematical programming Programming (Mathematics) Mathematical models Mathematisches Modell Modellierung (DE-588)4170297-9 gnd Anwendung (DE-588)4196864-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Modell (DE-588)4039798-1 gnd Lineare Optimierung (DE-588)4035816-1 gnd Methode (DE-588)4038971-6 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4170297-9 (DE-588)4196864-5 (DE-588)4114528-8 (DE-588)4039798-1 (DE-588)4035816-1 (DE-588)4038971-6 (DE-588)4043664-0 |
| title | Model building in mathematical programming |
| title_auth | Model building in mathematical programming |
| title_exact_search | Model building in mathematical programming |
| title_full | Model building in mathematical programming H. Paul Williams ; London school of economics, UK |
| title_fullStr | Model building in mathematical programming H. Paul Williams ; London school of economics, UK |
| title_full_unstemmed | Model building in mathematical programming H. Paul Williams ; London school of economics, UK |
| title_short | Model building in mathematical programming |
| title_sort | model building in mathematical programming |
| topic | Programming (Mathematics) Mathematical models Mathematisches Modell Modellierung (DE-588)4170297-9 gnd Anwendung (DE-588)4196864-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Modell (DE-588)4039798-1 gnd Lineare Optimierung (DE-588)4035816-1 gnd Methode (DE-588)4038971-6 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Programming (Mathematics) Mathematical models Mathematisches Modell Modellierung Anwendung Modell Lineare Optimierung Methode Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025720276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT williamshilaryp modelbuildinginmathematicalprogramming |