Markov decision processes in practice:
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| Language: | English |
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Cham, Switzerland
Springer
[2017]
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| Series: | International series in operations research & management science
volume 248 |
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| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xxxii, 550 Seiten |
| ISBN: | 9783319477640 |
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MARC
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| 245 | 1 | 0 | |a Markov decision processes in practice |c Richard J. Boucherie, Nico M. van Dijk (editors) |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2017] | |
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| adam_text | Contents
Part I General Theory
1 One-Step Improvement Ideas and Computational Aspects.............. 3
Henk Tijms
1.1 Introduction.............................................. 3
1.2 The Average-Cost Markov Decision Model....................... 4
1.2.1 The Concept of Relative Values....................... 6
1.2.2 The Policy-Improvement Step.......................... 8
1.2.3 The Odoni Bounds for Value Iteration................ 11
1.3 Tailor-Made Policy-Iteration Algorithm...................... 13
1.3.1 A Queueing Control Problem with a Variable Service
Rate................................................ 15
1.4 One-Step Policy Improvement for Suboptimai Policies......... 18
1.4.1 Dynamic Routing of Customers to Parallel Queues .... 19
1.5 One-Stage-Look-Ahead Rule in Optimal Stopping............... 24
1.5.1 Devil’s Penny Problem............................... 25
1.5.2 A Game of Dropping Balls into Bins.................. 27
1.5.3 The Chow-Robbins Game............................... 30
References....................................................... 31
2 Value Function Approximation in Complex Queueing Systems.......... 33
Sandjai Bhulai
2.1 Introduction................................................ 33
2.2 Difference Calculus for Markovian Birth-Death Systems....... 35
2.3 Value Functions for Queueing Systems....................... 40
2.3.1 TheM/Cox(r)/l Queue................................. 41
2.3.2 Special Cases of the M/Cox(r)/l Queue............... 42
2.3.3 The M/M/s Queue..................................... 44
2.3.4 The Blocking Costs in an M/M/s/s Queue.............. 45
2.3.5 Priority Queues..................................... 45
2.4 Application: Routing to Parallel Queues........................ 47
2.5 Application: Dynamic Routing in Multiskill Call Centers........ 52
2.6 Application: A Controlled Polling System....................... 60
References........................................................... 61
3 Approximate Dynamic Programming by Practical Examples................ 63
Martijn R.K. Mes and Arturo Pérez Rivera
3.1 Introduction................................................... 63
3.2 The Nomadic Trucker Example ................................... 66
3.2.1 Problem Introduction.................................. 67
3.2.2 MDP Model............................................ 67
3.2.3 Approximate Dynamic Programming....................... 69
3.3 A Freight Consolidation Example................................ 79
3.3.1 Problem Introduction.................................. 79
3.3.2 MDP Model............................................. 80
3.3.3 Approximate Dynamic Programming....................... 83
3.4 A Healthcare Example........................................... 90
3.4.1 Problem Introduction................................ 90
3.4.2 MDP Model............................................. 91
3.4.3 Approximate Dynamic Programming....................... 93
3.5 What’s More.................................................... 95
3.5.1 Policies............................................ 96
3.5.2 Value Function Approximations......................... 96
3.5.3 Exploration vs Exploitation........................... 97
. Appendix.............................................................. 97
References......................................................... 100
4 Server Optimization of Infinite Queueing Systems.....................103
András Mészáros and Miklós Telek
4.1 Introduction...................................................103
4.2 Basic Definition and Notations.................................105
4.3 Motivating Examples............................................106
4.3.1 Optimization of a Queueing System with Two Different
Servers...............................................106
4.3.2 Optimization of a Computational System with Power
Saving Mode...........................................107
4.3.3 Structural Properties of These Motivating Examples .... 109
4.4 Theoretical Background ........................................109
4.4.1 Subset Measures in Markov Chains .....................109
4.4.2 Markov Chain Transformation...........................112
4.4.3 Markov Decision Processes with a Set of Uncontrolled
States ...............................................114
4.4.4 Infinite Markov Chains with Regular Structure.........115
4.5 Solution and Numerical Analysis of the Motivating Examples .... 116
4.5.1 Solution to the Queue with Two Different Servers......116
4.5.2 Solution to the Power֊Saving Model....................117
4.6 Further Examples.............................................119
4.6.1 Optimization of a Queuing System with Two Markov
Modulated Servers ...................................120
4.6.2 Structural Properties of the Example with Markov
Modulated Servers ...................................120
4.7 Infinite MDPs with Quasi Birth Death Structure...............121
4.7.1 Quasi Birth Death Process............................121
4.7.2 Solving MDPs with QBD Structure .....................122
4.8 Solution and Numerical Analysis of MDPs with QBD Structure .. 127
4.8.1 Solution of the Example with Markov Modulated
Servers..............................................127
4.8.2 Markov Modulated Server with Three Background
States ..............................................128
4.9 Conclusion...................................................129
References..........................................................129
5 Structures of Optimal Policies in MDPs with Unbounded Jumps:
The State of Our Art................................................131
H. Blok and F.M. Spieksma
5.1 Introduction.............................................. 132
5.2 Discrete Time Model..........................................135
5.2.1 Discounted Cost......................................140
5.2.2 Approximations/Perturbations.........................146
5.2.3 Average Cost...................................... 151
5.3 Continuous Time Model .......................................160
5.3.1 Uniformisation.......................................161
5.3.2 Discounted Cost.................................... 162
5.3.3 Average Cost.........................................165
5.3.4 Roadmap to Structural Properties.....................166
5.3.5 Proofs...............................................171
5.3.6 Tauberian Theorem....................................178
Appendix: Notation .................................................182
References..........................................................183
Partll Healthcare
6 Markov Decision Processes for Screening and Treatment of Chronic
Diseases............................................................189
Lauren N. Steimle and Brian T. Denton
6.1 Introduction.............................................. 189
6.2 Background on Chronic Disease Modeling.......................191
6.3 Modeling Framework for Chronic Diseases .....................193
6.3.1 MDP and POMDP Model Formulation .....................193
6.3.2 Solution Methods and Structural Properties...........197
6.3.3 Model Validation.....................................199
6.4 MDP Model for Cardiovascular Risk Control in Patients with
Type 2 Diabetes...............................................200
6.4.1 MDP Model Formulation................................201
6.4.2 Results: Comparison of Optimal Policies Versus
Published Guidelines ................................205
6.5 POMDP for Prostate Cancer Screening...........................208
6.5.1 POMDP Model Formulation..............................210
6.5.2 Results: Optimal Belief-Based Screening Policy.......214
6.6 Open Challenges in MDPs for Chronic Disease...................215
6.7 Conclusions...................................................217
References..........................................................218
7 Stratified Breast Cancer Follow-Up Using a Partially Observable
MDP.................................................................223
J.W.M. Otten, A. Witteveen, I.M.H. Vliegen, S. Síesling, J.B. Timmer,
and M.J. IJzerman
7.1 Introduction..................................................224
7.2 Model Formulation.............................................225
7.2.1 Optimality Equations.................................228
7.2.2 Alternative Representation of the Optimality Equations .. 230
7.2.3 Algorithm............................................232
7.3 Model Parameters..............................................235
7.4 Results.......................................................236
7.4.1 Sensitivity Analyses.................................240
7.5 Conclusions and Discussion....................................241
Appendix: Notation .................................................243
References..........................................................243
8 Advance Patient Appointment Scheduling............................ 245
Antoine Saure and Martin L. Puterman
8.1 Introduction..................................................245
8.2 Problem Description...........................................247
8.3 Mathematical Formulation......................................248
8.3.1 Decision Epochs.................................... 248
8.3.2 State Space........................................ 249
8.3.3 Action Sets..........................................249
8.3.4 Transition Probabilities.............................250
8.3.5 Immediate Cost.......................................251
8.3.6 Optimality Equations.............................. 252
8.4 Solution Approach.............................................252
8.5 Practical Results.............................................257
8.5.1 Computerized Tomography Scan Appointment
Scheduling...........................................257
8.5.2 Radiation Therapy Treatment Scheduling ..............260
8.6 Discussion....................................................262
8.7 Open Challenges...............................................265
Appendix: Notation .................................................266
References........................................................ 266
9 Optimal Ambulance Dispatching ....................................269
C.J. Jagtenberg, S. Bhulai and R.D. van der Mei
9.1 Introduction..................................................270
9.1.1 Previous Work.........................................270
9.1.2 Our Contribution......................................271
9.2 Problem Formulation...........................................272
9.3 Solution Method: Markov Decision Process......................273
9.3.1 State Space......................................... 274
9.3.2 Policy Definition.....................................275
9.3.3 Rewards...............................................276
9.3.4 Transition Probabilities..............................277
9.3.5 Value Iteration.......................................278
9.4 Solution Method: Dynamic MEXCLP Heuristic for Dispatching .. 279
9.4.1 Coverage According to the MEXCLP Model................279
9.4.2 Applying MEXCLP to the Dispatch Process...............279
9.5 Results: A Motivating Example ................................280
9.5.1 Fraction of Late Arrivals ............................281
9.5.2 Average Response Time.................................282
9.6 Results: Region Flevoland.....................................282
9.6.1 Analysis of the MDP Solution for Flevoland............285
9.6.2 Results............................................. 287
9.7 Conclusion and Discussion................................... 289
9.7.1 Further Research.................................... 289
Appendix: Notation .................................................290
References..........................................................290
10 Blood Platelet Inventory Management..................................293
Rene Haijema, Nico M. van Dijk, and Jan van der Wal
10.1 Introduction..................................................294
10.1.1 Practical Motivation..................................294
10.1.2 SDP-Simulation Approach...............................295
10.1.3 Outline...............................................295
10.2 Literature....................................................296
10.3 SDP-Simulation Approach for the Stationary PPP................296
10.3.1 Steps of SDP-Simulation Approach......................296
10.3.2 Step 1 : SDP Model for Stationary PPP.................297
10.3.3 Case Studies..........................................299
10.4 Extended SDP-Simulation Approach for the Non-Stationary PPP . 300
10.4.1 Problem: Non-Stationary Production Breaks.............300
10.4.2 Extended SDP-Simulation Approach......................300
10.4.3 Extension: Including Non-Stationary Periods...........301
10.5 Case Study: Optimal Policy Around Breaks.....................303
10.5.1 Data.................................................303
10.5.2 Step I: Stationary Problem...........................304
10.5.3 Steps II to IV: Christmas and New Year’s Day.........306
10.5.4 Steps II to IV: 4֊Days Easter Weekend................310
10.5.5 Conclusions: Extended SDP-Simulation Approach........314
10.6 Discussion and Conclusions ..................................314
Appendix: Notation .............................................. 315
References.........................................................316
Partili Transportation
11 Stochastic Dynamic Programming for Noise Load Management .... 321
T.R. Meerburg, Richard J. Boucherie, and M.J.A.L. van Kraaij
11.1 Introduction.................................................322
11.2 Noise Load Management at Amsterdam Airport Schiphol..........323
11.3 SDP for Noise Load Optimisation .............................325
11.4 Numerical Approach ..........................................327
11.4.1 Transition Probabilities............................ 327
11.4.2 Discretisation.......................................328
11.5 Numerical Results............................................328
11.5.1 Probability of Exceeding the Noise Load Limit........329
11.5.2 Comparison with the Heuristic .......................330
11.5.3 Increasing the Number of Decision Epochs.............331
11.6 Discussion...................................................332
Appendix...........................................................333
References.........................................................335
12 Allocation in a Vertical Rotary Car Park............................337
M. Fackrell and P. Taylor
12.1 Introduction.................................................337
12.2 Background................................................. 340
12.2.1 The Car Parking Allocation Problem...................340
12.2.2 Markov Decision Processes............................344
12.3 The Markov Decision Process..................................345
12.4 Numerical Results............................................345
12.5 Simulation Results...........................................348
12.6 Conclusion...................................................352
Appendix...........................................................353
References.........................................................369
13 Dynamic Control of Traffic Lights....................................371
Rene Haijema, Eligius M.T. Hendrix, and Jan van der Wal
13.1 Problem.......................................................372
13.2 Markov Decision Process (MDP).................................373
13.2.1 Examples: Terminology and Notations...................373
13.2.2 MDP Model.............................................374
13.3 Approximation by Policy Iteration.............................376
13.3.1 Policy Iteration (PI)............................. 376
13.3.2 Initial Policy: Fixed Cycle (FC)......................377
13.3.3 Policy Evaluation Step of FC..........................377
13.3.4 Single Policy Improvement Step: RVI Policy............379
13.3.5 Computational Complexity of RVI.......................379
13.3.6 Additional Iterations of PI...........................381
13.4 Results..................................................... 381
13.4.1 Simulation............................................381
13.4.2 Intersection F4C2.....................................382
13.4.3 Complex Intersection F12C4............................382
13.5 Discussion and Conclusions ...................................384
Appendix: Notation .................................................385
References..........................................................386
14 Smart Charging of Electric Vehicles .................................387
Pia L. Kempker, Nico M. van Dijk, Werner Scheinhardt,
Hans van den Berg, and Johann Hurink
14.1 Introduction..................................................388
14.2 Background on DSM and PowerMatcher............................389
14.3 Optimal Charging Strategies...................................392
14.3.1 MDP/SDP Problem Formulation...........................393
14.3.2 Analytic Solution for i.i.d. Prices ..................395
14.3.3 DP-Heuristic Strategy............................. 398
14.4 Numerical Results.............................................399
14.5 Conclusion/Future Research....................................402
Appendix............................................................402
References.................................................... 403
Part IV Production
15 Analysis of a Stochastic Lot Scheduling Problem with Strict
Due-Dates...........................................................407
Nicky D. van Foreest and Jacob Wijngaard
15.1 Introduction..................................................407
15.2 Theoretical Background of the CSLSP...........................409
15.3 Production System, Admissible Policies, and Objective Function . 410
15.3.1 Production System ....................................410
15.3.2 Admissible Actions and Policies.......................411
15.3.3 Objective Function....................................412
15.4 The Markov Decision Process.....................................413
15.4.1 Format of a State......................................413
15.4.2 Actions and Operators .................................415
15.4.3 Transition Matrices....................................416
15.4.4 Further Aggregation in the Symmetric Case..............417
15.4.5 State Space............................................417
15.4.6 A Heuristic Threshold Policy...........................417
15.5 Numerical Study.................................................418
15.5.1 Influence of the Load and the Due-Date Horizon.........419
15.5.2 Visualization of the Structure of the Optimal Policy.419
15.6 Conclusion......................................................421
Appendix: Notation ...................................................421
References............................................................422
16 Optimal Fishery Policies............................................ 425
Eligius M.T. Hendrix, Rene Haijema, and Diana van Dijk
16.1 Introduction....................................................426
16.2 Model Description...............................................427
16.2.1 Biological Dynamics; Growth of Biomass.................427
16.2.2 Economic Dynamics; Harvest and Investment
Decisions..............................................428
16.2.3 Optimization Model.....................................429
16.3 Model Analysis..................................................430
16.3.1 Bounds on Decision and State Space ....................430
16.3.2 Equilibrium State Values in a Deterministic Setting..431
16.4 Discretization in the Value Iteration Approach..................432
16.4.1 Deterministic Elaboration..............................433
16.4.2 Stochastic Implementation..............................434
16.4.3 Analysis of the Stochastic Model.................. 435
16.5 Conclusions.....................................................436
Appendix: Notation.................................................. 438
References............................................................438
17 Near-Optimal Switching Strategies for a Tandem Queue..................439
Daphne van Leeuwen and Rudesindo Nühez-Queija
17.1 Introduction ...................................................440
17.2 Model Description: Single Service Model.........................442
17.3 Structural Properties of an Optimal Switching Curve.............444
17.4 Matrix Geometric Method for Fixed Threshold Policies............447
17.5 Model Description: Batch Transition Model.......................450
17.5.1 Structural Properties of the Batch Service Model.....451
17.5.2 Matrix Geometric Method with Batch Services............452
17.6 Simulation Experiments..........................................454
17.7 Conclusion......................................................456
References.......................................................... 458
PartV Communications
18 Wireless Channel Selection with Restless Bandits....................463
Julia Kuhn and Yoni Nazarathy
18.1 introduction.............................................. 464
18.2 Reward-Observing Restless Multi-Armed Bandits................466
18.3 Index Policies and the Whittle Index ........................471
18.4 Numerical Illustration and Evaluation........................476
18.5 Literature Survey ...........................................480
References.........................................................483
19 Flexible Staffing for Call Centers with Non-stationary Arrival
Rates..............................................................487
Alex Roubos, Sandjai Bhulai, and Ger Koole
19.1 Introduction.................................................487
19.2 Problem Formulation..........................................490
19.3 Solution Approach............................................491
19.4 Numerical Experiments........................................492
19.4.1 Constant Arrival Rate................................493
19.4.2 Time-Dependent Arrival Rate..........................495
19.4.3 Unknown Arrival Rate.................................497
19.5 Conclusion and Discussion....................................499
Appendix: Exact Solution...........................................500
References....................................................... 502
20 MDP for Query-Based Wireless Sensor Networks........................505
Mihaela Mitici
20.1 Problem Description..........................................506
20.2 Model Formulation............................................507
20.3 Continuous Time Markov Decision Process with a Drift.........508
20.4 Exponentially Uniformized Markov Decision Process............510
20.5 Discrete Time and Discrete Space Markov Decision Problem....511
20.6 Standard Markov Decision Process ............................513
20.7 Fixed Assignment Policies....................................514
20.7.1 Always Assign Queries to the DB......................514
20.7.2 Always Assign Queries to the WSN.....................514
20.8 Numerical Results.......................................... 515
20.8.1 Performance of Fixed Policies vs. Optimal Policy.....515
20.8.2 Optimal Policy Under Different Values
of the Uniformization Parameter......................515
20.9 Conclusion...................................................516
Appendices.........................................................516
References.........................................................518
Part VI Financial Modeling
21 Optimal Portfolios and Pricing of Financial Derivatives Under
Proportional Transaction Costs....................................523
Jorn Sass and Manfred Schal
21.1 Introduction................................................523
21.2 The Financial Model ........................................527
21.3 The Markov Decision Model...................................528
21.4 Martingale Properties of the Optimal Markov Decision Process... 531
21.5 Price Systems and the Numeraire Portfolio...................533
21.6 Conclusive Remarks..........................................535
Appendices........................................................537
References........................................................545
Appendix A: Basic Notation for MDP.....................................547
Appendix B: Dichotomy and Criteria.....................................549
i His book presents classical Markov Decision Processes (Ml)P) for real-life applications
and optimization. MDP allows users to develop and formally support approximate and
simple decision rules, and this book showcases state-of-the-art applications in which
MDP was key to the solution approach. Ihe book is divided into six parts. Part i is
devoted to the state-of-the-art theoretical foundation of MDP, including approximate
methods such as policy improvement, successive approximation and infinite state
spaces as well as an instructive chapter on Approximate Dynamic Programming. It
then continues with five parts of specific and non-exhaustivc application areas. Part 2
covers MDP healthcare applications, which includes different screening procedures,
appointment scheduling, ambulance scheduling and blood management. Part 3
explores MDP modeling within transportation, dins ranges from public to private
transportation, from airports and trallic lights to car parking or charging your electric
car. Part 4 contains three chapters that illustrates the structure of approximate policies
for production or manufacturing structures, in Part 5, communications is highlighted
as an important application area for MDP. it includes Ciittins indices, down-to-earth call
centers and wireless sensor networks, finally Part 6 is dedicated to financial modelim;,
olfering an instructive review to account for financial portfolios and derivatives under
proportional transactional costs. Ihe MDP applications in this book illustrate a variety
of both standard and non-standard aspects of MDP modeling and its practical use. 1 his
book should appeal to readers for practilioning, academic research and educational
purposes, with a background in, among others, operations research, mathematics,
computer science, and industrial engineering.
|
| any_adam_object | 1 |
| author2 | Boucherie, Richard J. 1964- Dijk, Nico M. van 1956- |
| author2_role | edt edt |
| author2_variant | r j b rj rjb n m v d nmv nmvd |
| author_GND | (DE-588)171417194 (DE-588)141300485 |
| author_facet | Boucherie, Richard J. 1964- Dijk, Nico M. van 1956- |
| building | Verbundindex |
| bvnumber | BV044258928 |
| classification_rvk | QH 237 QH 400 SK 820 |
| ctrlnum | (OCoLC)992431078 (DE-599)BVBBV044258928 |
| discipline | Mathematik Wirtschaftswissenschaften |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV044258928 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:48:00Z |
| institution | BVB |
| isbn | 9783319477640 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029663916 |
| oclc_num | 992431078 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-83 |
| physical | xxxii, 550 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Springer |
| record_format | marc |
| series | International series in operations research & management science |
| series2 | International series in operations research & management science |
| spelling | Markov decision processes in practice Richard J. Boucherie, Nico M. van Dijk (editors) Cham, Switzerland Springer [2017] xxxii, 550 Seiten txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science volume 248 Markov-Entscheidungsprozess (DE-588)4168927-6 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Markov-Entscheidungsprozess (DE-588)4168927-6 s DE-604 Boucherie, Richard J. 1964- (DE-588)171417194 edt Dijk, Nico M. van 1956- (DE-588)141300485 edt International series in operations research & management science volume 248 (DE-604)BV011630976 248 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029663916&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029663916&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Markov decision processes in practice International series in operations research & management science Markov-Entscheidungsprozess (DE-588)4168927-6 gnd |
| subject_GND | (DE-588)4168927-6 (DE-588)4143413-4 |
| title | Markov decision processes in practice |
| title_auth | Markov decision processes in practice |
| title_exact_search | Markov decision processes in practice |
| title_full | Markov decision processes in practice Richard J. Boucherie, Nico M. van Dijk (editors) |
| title_fullStr | Markov decision processes in practice Richard J. Boucherie, Nico M. van Dijk (editors) |
| title_full_unstemmed | Markov decision processes in practice Richard J. Boucherie, Nico M. van Dijk (editors) |
| title_short | Markov decision processes in practice |
| title_sort | markov decision processes in practice |
| topic | Markov-Entscheidungsprozess (DE-588)4168927-6 gnd |
| topic_facet | Markov-Entscheidungsprozess Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029663916&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029663916&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011630976 |
| work_keys_str_mv | AT boucherierichardj markovdecisionprocessesinpractice AT dijknicomvan markovdecisionprocessesinpractice |