Operations research: introduction to models and methods
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New Jersey ; London
World Scientific
[2022]
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 499 Seiten Diagramme |
| ISBN: | 9789811239342 9789811239816 |
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| 245 | 1 | 0 | |a Operations research |b introduction to models and methods |c Richard J. Boucherie (University of Twente, The Netherlands), Aleida Braaksma (University of Twente, The Netherlands), Henk Tijms (Vrije University Amsterdam, The Netherlands) |
| 264 | 1 | |a New Jersey ; London |b World Scientific |c [2022] | |
| 264 | 4 | |c ©2022 | |
| 300 | |a xii, 499 Seiten |b Diagramme | ||
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Datensatz im Suchindex
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| adam_text | Contents Preface v 1. Linear Programming 1 1.1 1.2 1 2 3 5 6 7 9 13 13 15 16 18 20 22 32 32 1.3 1.4 1.5 1.6 1.7 1.8 Introduction......................................................................................... The Formulation of LP Models........................................................ 1.2.1 A Production Planning Problem.......................................... 1.2.2 A Nonlinear Programming Problem.................................... 1.2.3 A Distribution Problem........................................................ 1.2.4 Graphical Solution Method for LP....................................... 1.2.5 General Formulation of an LP Model................................. Linear Programming Applications...................................................... 1.3.1 An Investment Problem........................................................ 1.3.2 A Currency Problem ........................................................... 1.3.3 A Cutting Stock Problem...................................................... 1.3.4 Two-Finger Morra................................................................. 1.3.5 Fitting Curves....................................................................... The Simplex Method.......................................................................... The Dual LP Problem....................................................................... 1.5.1 An Illustrative Example......................................................... 1.5.2 Economic Interpretation of the Dual: Shadow Prices and Reduced
Costs....................................................................... 1.5.3 The General Dual LP Problem............................................ Sensitivity Analysis............................................................................. 1.6.1 Computer Output for Sensitivity Analysis........................... 1.6.2 A Production Planning Problem.......................................... 1.6.3 A Feed Mixing Problem......................................................... 1.6.4 Computational Method forSensitivity Analysis................... Linear Programming with Matrix Algebra....................................... Exercises............................................................................................... vii 37 39 42 42 46 49 53 57 65
Operations Research: Introduction to Models and Methods viii 2. Integer Programming 81 2.1 2.2 Introduction.............................................................................................. 81 Applications of Integer Programming.................................................. 83 2.2.1 An Investment Problem............................................................ 83 2.2.2 A Location Problem.................................................................. 86 2.2.3 A Distribution Problem............................................................ 88 2.2.4 A Timetabling Problem............................................................ 91 2.2.5 A Partitioning Problem............................................................ 94 2.2.6 A Production-Stock Problem.................................................. 95 2.3 General Modeling Tricks........................................................................ 97 2.4 The Branch-and-Bound Method...............................................................100 2.5 Cutting Plane Methods ........................................................................... 104 2.6 Lagrangian Relaxation.............................................................................. 105 2.7 Heuristics.................................................................................................110 2.7.1 A Partitioning Problem...............................................................110 2.7.2 A Container Loading Problem.................................................. 110 2.7.3 The Set-Covering
Problem........................................................ Ill 2.7.4 The Facility Location Problem.................................................. 114 2.8 The Traveling Salesman Problem........................................................... 115 2.9 A Routing Problem.................................................................................... 123 2.10 Exercises.......................................................................................................127 3. Network Analysis 3.1 3.2 3.3 3.4 3.5 3.6 4. Shortest-Path Problems...........................................................................134 Maximum-Flow Problems........................................................................143 Minimum Spanning Trees........................................................................150 Minimum-Cost Flow Problems .............................................................. 157 3.4.1 A Transportation Problem........................................................ 158 3.4.2 An Assignment Problem ........................................................... 159 Euler Circuit and the Chinese Postman Problem............................... 162 3.5.1 Euler Circuit................................................................................. 162 3.5.2 The Chinese Postman Problem.................................................. 165 Exercises.......................................................................................................169 Decision Trees 4.1 4.2 133 175 Tree Diagrams
.......................................................................................... 175 4.1.1 The Monty Hall Problem........................................................... 175 4.1.2 The Test Paradox....................................................................... 178 4.1.3 Bayes’ Rule in Odds Form ........................................................ 182 Decision Trees............................................................................................. 184 4.2.1 A Choice Problem....................................................................... 185 4.2.2 An Oil Drilling Problem.............................................................. 187
ix Contents 4.3 5. Dynamic Programming 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6. Exercises.................................................................................................. 190 Introduction............................................................................................ 193 Shortest Path in a Manhattan Network.............................................. 196 Flexibility of Dynamic Programming.................................................... 199 5.3.1 General Structure of Dynamic Programming Problems . . 199 5.3.2 The Safest Path.......................................................................200 5.3.3 The Minimax Optimal Path .................................................... 202 Shortest Path in an Acyclic Network................................................. 204 Applications of the Acyclic Network.................................................... 206 5.5.1 A Replacement Problem .......................................................... 206 5.5.2 A Production-Stock Problem.................................................... 208 5.5.3 The Knapsack Problem............................................................. 209 An Allocation Problem..........................................................................211 The General Shortest-Path Problem.................................................... 213 Stochastic Dynamic Programming ....................................................... 215 5.8.1 General Structure of Stochastic Dynamic Programming . . 215 5.8.2 A Dice Game and Optimal
Stopping........................................216 5.8.3 Roulette: Betting Red or Black .............................................. 218 5.8.4 The Kelly Strategy for an Investment Problem..................... 219 5.8.5 The Dice Game Pig....................................................................221 5.8.6 Optimal Stopping and the One-Stage-Look-Ahead Rule . . 222 Exercises..................................................................................................... 225 Inventory Management 6.1 6.2 6.3 6.4 6.5 193 233 The EOQ Model and the EPQ Model ................................................. 234 6.1.1 The Formula for the EOQ Inventory Model............................234 6.1.2 Quantity Discount.......................................................................237 6.1.3 The Exchange Curve ................................................................ 238 6.1.4 The EPQ Production Model.................................................... 240 The Silver-Meal Heuristic.......................................................................243 The News Vendor Problem.......................................................................245 6.3.1 Discretely Distributed Demand................................................. 246 6.3.2 Continuously Distributed Demand...........................................249 6.3.3 The News Vendor Problem with Multiple Products .... 252 Stochastic Inventory Models....................................................................254 6.4.1 The (s, Q) Continuous Review Inventory Model .................. 255 6.4.2 The
(s, Q) Model with Lost Sales ...........................................264 6.4.3 The (R, S) Periodic Review Inventory Model.........................265 6.4.4 The (R, s, S) Inventory Model................................................. 268 Exercises......................................................................................................270
Operations Research: Introduction to Models and Methods x 7. Discrete-Time Markov Chains 7.1 7.2 7.3 7.4 7.5 7.6 8. 8.7 8.8 9. Introduction.................................................................................................277 The Discrete-Time Markov Chain.............................................................278 Time-Dependent Behavior.........................................................................283 7.3.1 Transient and Recurrent States.................................................. 285 7.3.2 Mean First Passage Times ........................................................ 287 7.3.3 Absorbing Markov Chains ........................................................ 288 Equilibrium and Stationary Probabilities................................................293 7.4.1 Limiting Behavior........................................................................294 7.4.2 Balance Equations........................................................................295 7.4.3 Markov Chains with a Cost Structure......................................298 Markov Chain Monte Carlo Method ..................................................... 300 7.5.1 Reversible Markov Chains ........................................................ 300 7.5.2 The Metropolis-Hastings Algorithm.........................................303 7.5.3 The Gibbs Sampler.....................................................................307 Exercises...................................................................................................... 310 Continuous-Time Markov Chains 8.1 8.2
8.3 8.4 8.5 8.6 9.3 9.4 315 Introduction................................................................................................ 315 The Continuous-Time Markov Chain..................................................... 316 Transient Probabilities..............................................................................321 The Uniformization Method.................................................................... 323 Equilibrium Probabilities ....................................................................... 327 Birth and Death Process.......................................................................... 332 8.6.1 Equilibrium Distribution........................................................... 333 8.6.2 First Entrance Times................................................................. 334 Applications to Queueing Systems ........................................................ 334 8.7.1 The Single-Server Queue........................................................... 334 8.7.2 The Erlang Loss Model.............................................................. 338 8.7.3 Recursive Calculation ofthe Equilibrium Probabilities . . . 340 Exercises...................................................................................................... 341 Queueing Theory 9.1 9.2 277 347 Introduction................................................................................................347 Basic Elements..........................................................................................350 9.2.1 Queue
Characteristics................................................................. 351 9.2.2 Data Analysis............................................................................. 352 Fundamental Queueing Results..............................................................354 9.3.1 Little’s Law ................................................................................ 354 9.3.2 Poisson Arrivals See TimeAverages (PASTA) ....................... 357 9.3.3 Regenerative Stochastic Processes........................................... 359 Queueing Formulas................................................................................... 361
Contents 9.5 9.6 xi 9.4.1 The M/M/1 Queue....................................................................362 9.4.2 The М/G/1 Queue....................................................................365 9.4.3 The M/G/l Queue with Priorities...........................................368 9.4.4 The M/M/c Queue....................................................................370 9.4.5 The M/G/c Queue ....................................................................374 9.4.6 The M/G/c/c Queue (the Erlang Loss Model)..................... 375 9.4.7 The M/G/oo Queue....................................................................377 9.4.8 The M/M/c/c + N Queue....................................................... 378 9.4.9 The M/M/c Queue and CallCenters...................................... 381 Networks of Queues................................................................................... 385 9.5.1 Tandem Queues..........................................................................385 9.5.2 An Open Network of Queues.................................................... 388 9.5.3 A Closed Network of Queues.................................................... 392 Exercises..................................................................................................... 395 10. Markov Decision Processes 401 10.1 Introduction............................................................................................... 401 10.1.1 Discounting and Present Value................................................. 401 10.2 Markov Decision
Processes.......................................................................402 10.3 Markov Decision Processes: Discounted Rewards...............................404 10.3.1 Value Iteration.............................................................................409 10.3.2 Policy Iteration ..........................................................................412 10.3.3 Linear Programming....................................................................415 10.4 Markov Decision Processes: Average Rewards..................................... 417 10.4.1 Linear Programming....................................................................418 10.5 Exercises......................................................................................................420 11. Simulation 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 427 Introduction............................................................................................... 427 Discrete-Event Simulation.......................................................................429 Random Number Generator....................................................................433 Short-Term Simulation.............................................................................438 11.4.1 Statistical Analysis ....................................................................438 Long-Term Simulation.............................................................................445 Random Samples from Probability Distributions ...............................451 11.6.1 The Acceptance-Rejection
Method...........................................451 11.6.2 The Inversion Sampling Method for Discrete Densities . . . 453 Variance-Reduction Methods .................................................................456 11.7.1 Common Random Numbers....................................................... 456 11.7.2 Conditional Monte Carlo.......................................................... 459 11.7.3 Importance Sampling.................................................................460 Exercises......................................................................................................462
xii Operations Research: Introduction to Models and Methods Appendix A Complexity Theory 459 Appendix В 473 Useful Formulas for the Normal Distribution Appendix C The Poisson Process 475 Appendix D Answers to Selected Exercises 487 Index 497
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Contents Preface v 1. Linear Programming 1 1.1 1.2 1 2 3 5 6 7 9 13 13 15 16 18 20 22 32 32 1.3 1.4 1.5 1.6 1.7 1.8 Introduction. The Formulation of LP Models. 1.2.1 A Production Planning Problem. 1.2.2 A Nonlinear Programming Problem. 1.2.3 A Distribution Problem. 1.2.4 Graphical Solution Method for LP. 1.2.5 General Formulation of an LP Model. Linear Programming Applications. 1.3.1 An Investment Problem. 1.3.2 A Currency Problem . 1.3.3 A Cutting Stock Problem. 1.3.4 Two-Finger Morra. 1.3.5 Fitting Curves. The Simplex Method. The Dual LP Problem. 1.5.1 An Illustrative Example. 1.5.2 Economic Interpretation of the Dual: Shadow Prices and Reduced
Costs. 1.5.3 The General Dual LP Problem. Sensitivity Analysis. 1.6.1 Computer Output for Sensitivity Analysis. 1.6.2 A Production Planning Problem. 1.6.3 A Feed Mixing Problem. 1.6.4 Computational Method forSensitivity Analysis. Linear Programming with Matrix Algebra. Exercises. vii 37 39 42 42 46 49 53 57 65
Operations Research: Introduction to Models and Methods viii 2. Integer Programming 81 2.1 2.2 Introduction. 81 Applications of Integer Programming. 83 2.2.1 An Investment Problem. 83 2.2.2 A Location Problem. 86 2.2.3 A Distribution Problem. 88 2.2.4 A Timetabling Problem. 91 2.2.5 A Partitioning Problem. 94 2.2.6 A Production-Stock Problem. 95 2.3 General Modeling Tricks. 97 2.4 The Branch-and-Bound Method.100 2.5 Cutting Plane Methods . 104 2.6 Lagrangian Relaxation. 105 2.7 Heuristics.110 2.7.1 A Partitioning Problem.110 2.7.2 A Container Loading Problem. 110 2.7.3 The Set-Covering
Problem. Ill 2.7.4 The Facility Location Problem. 114 2.8 The Traveling Salesman Problem. 115 2.9 A Routing Problem. 123 2.10 Exercises.127 3. Network Analysis 3.1 3.2 3.3 3.4 3.5 3.6 4. Shortest-Path Problems.134 Maximum-Flow Problems.143 Minimum Spanning Trees.150 Minimum-Cost Flow Problems . 157 3.4.1 A Transportation Problem. 158 3.4.2 An Assignment Problem . 159 Euler Circuit and the Chinese Postman Problem. 162 3.5.1 Euler Circuit. 162 3.5.2 The Chinese Postman Problem. 165 Exercises.169 Decision Trees 4.1 4.2 133 175 Tree Diagrams
. 175 4.1.1 The Monty Hall Problem. 175 4.1.2 The Test Paradox. 178 4.1.3 Bayes’ Rule in Odds Form . 182 Decision Trees. 184 4.2.1 A Choice Problem. 185 4.2.2 An Oil Drilling Problem. 187
ix Contents 4.3 5. Dynamic Programming 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6. Exercises. 190 Introduction. 193 Shortest Path in a Manhattan Network. 196 Flexibility of Dynamic Programming. 199 5.3.1 General Structure of Dynamic Programming Problems . . 199 5.3.2 The Safest Path.200 5.3.3 The Minimax Optimal Path . 202 Shortest Path in an Acyclic Network. 204 Applications of the Acyclic Network. 206 5.5.1 A Replacement Problem . 206 5.5.2 A Production-Stock Problem. 208 5.5.3 The Knapsack Problem. 209 An Allocation Problem.211 The General Shortest-Path Problem. 213 Stochastic Dynamic Programming . 215 5.8.1 General Structure of Stochastic Dynamic Programming . . 215 5.8.2 A Dice Game and Optimal
Stopping.216 5.8.3 Roulette: Betting Red or Black . 218 5.8.4 The Kelly Strategy for an Investment Problem. 219 5.8.5 The Dice Game Pig.221 5.8.6 Optimal Stopping and the One-Stage-Look-Ahead Rule . . 222 Exercises. 225 Inventory Management 6.1 6.2 6.3 6.4 6.5 193 233 The EOQ Model and the EPQ Model . 234 6.1.1 The Formula for the EOQ Inventory Model.234 6.1.2 Quantity Discount.237 6.1.3 The Exchange Curve . 238 6.1.4 The EPQ Production Model. 240 The Silver-Meal Heuristic.243 The News Vendor Problem.245 6.3.1 Discretely Distributed Demand. 246 6.3.2 Continuously Distributed Demand.249 6.3.3 The News Vendor Problem with Multiple Products . 252 Stochastic Inventory Models.254 6.4.1 The (s, Q) Continuous Review Inventory Model . 255 6.4.2 The
(s, Q) Model with Lost Sales .264 6.4.3 The (R, S) Periodic Review Inventory Model.265 6.4.4 The (R, s, S) Inventory Model. 268 Exercises.270
Operations Research: Introduction to Models and Methods x 7. Discrete-Time Markov Chains 7.1 7.2 7.3 7.4 7.5 7.6 8. 8.7 8.8 9. Introduction.277 The Discrete-Time Markov Chain.278 Time-Dependent Behavior.283 7.3.1 Transient and Recurrent States. 285 7.3.2 Mean First Passage Times . 287 7.3.3 Absorbing Markov Chains . 288 Equilibrium and Stationary Probabilities.293 7.4.1 Limiting Behavior.294 7.4.2 Balance Equations.295 7.4.3 Markov Chains with a Cost Structure.298 Markov Chain Monte Carlo Method . 300 7.5.1 Reversible Markov Chains . 300 7.5.2 The Metropolis-Hastings Algorithm.303 7.5.3 The Gibbs Sampler.307 Exercises. 310 Continuous-Time Markov Chains 8.1 8.2
8.3 8.4 8.5 8.6 9.3 9.4 315 Introduction. 315 The Continuous-Time Markov Chain. 316 Transient Probabilities.321 The Uniformization Method. 323 Equilibrium Probabilities . 327 Birth and Death Process. 332 8.6.1 Equilibrium Distribution. 333 8.6.2 First Entrance Times. 334 Applications to Queueing Systems . 334 8.7.1 The Single-Server Queue. 334 8.7.2 The Erlang Loss Model. 338 8.7.3 Recursive Calculation ofthe Equilibrium Probabilities . . . 340 Exercises. 341 Queueing Theory 9.1 9.2 277 347 Introduction.347 Basic Elements.350 9.2.1 Queue
Characteristics. 351 9.2.2 Data Analysis. 352 Fundamental Queueing Results.354 9.3.1 Little’s Law . 354 9.3.2 Poisson Arrivals See TimeAverages (PASTA) . 357 9.3.3 Regenerative Stochastic Processes. 359 Queueing Formulas. 361
Contents 9.5 9.6 xi 9.4.1 The M/M/1 Queue.362 9.4.2 The М/G/1 Queue.365 9.4.3 The M/G/l Queue with Priorities.368 9.4.4 The M/M/c Queue.370 9.4.5 The M/G/c Queue .374 9.4.6 The M/G/c/c Queue (the Erlang Loss Model). 375 9.4.7 The M/G/oo Queue.377 9.4.8 The M/M/c/c + N Queue. 378 9.4.9 The M/M/c Queue and CallCenters. 381 Networks of Queues. 385 9.5.1 Tandem Queues.385 9.5.2 An Open Network of Queues. 388 9.5.3 A Closed Network of Queues. 392 Exercises. 395 10. Markov Decision Processes 401 10.1 Introduction. 401 10.1.1 Discounting and Present Value. 401 10.2 Markov Decision
Processes.402 10.3 Markov Decision Processes: Discounted Rewards.404 10.3.1 Value Iteration.409 10.3.2 Policy Iteration .412 10.3.3 Linear Programming.415 10.4 Markov Decision Processes: Average Rewards. 417 10.4.1 Linear Programming.418 10.5 Exercises.420 11. Simulation 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 427 Introduction. 427 Discrete-Event Simulation.429 Random Number Generator.433 Short-Term Simulation.438 11.4.1 Statistical Analysis .438 Long-Term Simulation.445 Random Samples from Probability Distributions .451 11.6.1 The Acceptance-Rejection
Method.451 11.6.2 The Inversion Sampling Method for Discrete Densities . . . 453 Variance-Reduction Methods .456 11.7.1 Common Random Numbers. 456 11.7.2 Conditional Monte Carlo. 459 11.7.3 Importance Sampling.460 Exercises.462
xii Operations Research: Introduction to Models and Methods Appendix A Complexity Theory 459 Appendix В 473 Useful Formulas for the Normal Distribution Appendix C The Poisson Process 475 Appendix D Answers to Selected Exercises 487 Index 497 |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV047646929 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:48:58Z |
| indexdate | 2024-07-10T09:18:12Z |
| institution | BVB |
| isbn | 9789811239342 9789811239816 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033031053 |
| oclc_num | 1285001792 |
| open_access_boolean | |
| owner | DE-384 DE-29T DE-355 DE-BY-UBR DE-945 DE-N2 DE-1050 DE-703 DE-91G DE-BY-TUM DE-898 DE-BY-UBR DE-521 |
| owner_facet | DE-384 DE-29T DE-355 DE-BY-UBR DE-945 DE-N2 DE-1050 DE-703 DE-91G DE-BY-TUM DE-898 DE-BY-UBR DE-521 |
| physical | xii, 499 Seiten Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Boucherie, Richard J. 1964- Verfasser (DE-588)171417194 aut Operations research introduction to models and methods Richard J. Boucherie (University of Twente, The Netherlands), Aleida Braaksma (University of Twente, The Netherlands), Henk Tijms (Vrije University Amsterdam, The Netherlands) New Jersey ; London World Scientific [2022] ©2022 xii, 499 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Operations Research (DE-588)4043586-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Operations Research (DE-588)4043586-6 s DE-604 Braaksma, Aleida Verfasser (DE-588)1077453817 aut Tijms, Henk C. 1944- Verfasser (DE-588)114608474 aut Erscheint auch als Online-Ausgabe 978-981-123-935-9 (DE-604)BV047711541 Erscheint auch als Online-Ausgabe 978-981-123-936-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033031053&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boucherie, Richard J. 1964- Braaksma, Aleida Tijms, Henk C. 1944- Operations research introduction to models and methods Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4043586-6 (DE-588)4151278-9 |
| title | Operations research introduction to models and methods |
| title_auth | Operations research introduction to models and methods |
| title_exact_search | Operations research introduction to models and methods |
| title_exact_search_txtP | Operations research introduction to models and methods |
| title_full | Operations research introduction to models and methods Richard J. Boucherie (University of Twente, The Netherlands), Aleida Braaksma (University of Twente, The Netherlands), Henk Tijms (Vrije University Amsterdam, The Netherlands) |
| title_fullStr | Operations research introduction to models and methods Richard J. Boucherie (University of Twente, The Netherlands), Aleida Braaksma (University of Twente, The Netherlands), Henk Tijms (Vrije University Amsterdam, The Netherlands) |
| title_full_unstemmed | Operations research introduction to models and methods Richard J. Boucherie (University of Twente, The Netherlands), Aleida Braaksma (University of Twente, The Netherlands), Henk Tijms (Vrije University Amsterdam, The Netherlands) |
| title_short | Operations research |
| title_sort | operations research introduction to models and methods |
| title_sub | introduction to models and methods |
| topic | Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Operations Research Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033031053&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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