Capacitated planned maintenance: models, optimization algorithms, combinatorial and polyhedral properties
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
[Cham, Schweiz]
Springer
[2017]
|
| Schriftenreihe: | Lecture notes in economics and mathematical systems
686 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxix, 286 Seiten Diagramme 24 cm |
| ISBN: | 9783319402888 |
Internformat
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| 100 | 1 | |a Kuschel, Torben |e Verfasser |0 (DE-588)1052819419 |4 aut | |
| 245 | 1 | 0 | |a Capacitated planned maintenance |b models, optimization algorithms, combinatorial and polyhedral properties |c Torben Kuschel |
| 264 | 1 | |a [Cham, Schweiz] |b Springer |c [2017] | |
| 300 | |a xxix, 286 Seiten |b Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in economics and mathematical systems |v 686 | |
| 502 | |b Dissertation |c Bergische Universität Wuppertal | ||
| 505 | 8 | |a Includes bibliographical references and index | |
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Datensatz im Suchindex
| _version_ | 1804176816151199744 |
|---|---|
| adam_text | Contents
1 Introduction........................................................ 1
References.......................................................... 5
2 The Capacitated Planned Maintenance Problem ........................ 7
2.1 Problem Definition and Motivation............................. 7
2.2 Known Maintenance Problems................................... 10
2.2.1 Periodic Maintenance................................ 10
2.2.2 Machine Scheduling with Periodic Maintenance.......... 11
2.2.3 Periodic Maintenance Inspection....................... 12
2.2.4 Aircraft Maintenance.................................. 13
2.2.5 Other Maintenance Approaches.......................... 13
2.3 The Mathematical Formulation................................. 15
2.3.1 Assumptions and Terminology .......................... 17
2.3.2 Data Structure........................................ 19
References......................................................... 21
3 Known Concepts and Solution Techniques ........................... 25
3.1 Computational Complexity..................................... 25
3.2 Linear and Integer Programming............................... 27
3.2.1 The Simplex Algorithm................................. 34
3.2.2 The Primal-Dual Simplex Algorithm..................... 34
3.3 Dual Decomposition: Lagrangean Relaxation.................... 35
3.3.1 Column Generation..................................... 41
3.3.2 Subgradient Optimization.............................. 43
3.4 Primal Decomposition: Benders Reformulation................. 49
3.5 Local Search and Tabu Search................................. 52
3.5.1 Local Search........................................ 52
3.5.2 Tabu Search........................................... 53
3.6 The Knapsack Problem......................................... 55
3.6.1 Valid Inequalities.................................. 56
3.6.2 Lower and Upper Bounds................................ 59
3.6.3 An Exact Algorithm.................................... 62
References......................................................... 65
IX
4 The Weighted Uncapacitated Planned Maintenance Problem............. 71
4.1 The Mathematical Formulation................................. 71
4.2 Polyhedral Properties........................................ 74
4.3 Computational Complexity..................................... 82
4.4 The Single Weighted Uncapacitated Planned
Maintenance Problem.......................................... 89
4.4.1 An Optimal Solution to the Primal Problem............. 89
4.4.2 An Optimal Solution to the Corresponding Dual
Problem of the LP Relaxation............................ 91
4.5 The Uncapacitated Planned Maintenance Problem................ 94
References......................................................... 101
5 Analyzing the Solvability of the Capacitated Planned
Maintenance Problem................................................ 103
5.1 Valid Inequalities and Polyhedral Properties.................. 103
5.2 Computational Complexity...................................... 112
5.3 Lower Bounds.................................................. 127
5.3.1 Considered Lower Bounds................................ 127
5.3.2 Relative Strengths and Computational Complexity........ 133
5.3.3 Transformations of the Lower Bounds................... 144
5.3.3.1 Network Flow Problems........................ 145
5.3.3.2 Facility Location Problems................... 147
5.3.4 Mathematical Formulations of the Lagrangean Duals..... 150
5.3.4.1 Lagrangean Duals Z^+(Q)
and Z^X)+(Q) ................................. 150
5.3.4.2 Lagrangean Dual Z(p) ....................... 154
5.3.4.3 Lagrangean Dual Z(o .......................... 156
5.3.4.4 Lagrangean Dual Z(p)/(c ..................... 157
5.3.4.5 Lagrangean Dual Z^y] ......................... 161
References......................................................... 162
6 Algorithms for the Capacitated Planned Maintenance Problem......... 165
6.1 Three Construction Heuristics................................. 165
6.1.1 The First Fit Heuristic................................ 166
6.1.2 The Overlap Heuristic.................................. 167
6.1.3 The Iterated Best-of-Three Heuristic................... 170
6.2 Two Lagrangean Heuristics..................................... 170
6.2.1 The Lagrangean Relaxation of the Capacity Constraint.. 171
6.2.1.1 The LP Lower Bound .......................... 172
6.2.1.2 The Dual Priority Rule Lower Bound........... 174
6.2.1.3 The Combined Lower Bound...................... 176
6.2.1.4 The Primal-Dual Lower Bound................... 176
6.2.1.5 The Shortest Path Lower Bound................. 183
6.2.1.6 The Upper Bound Heuristic..................... 183
6.2.2 The Lagrangean Relaxation of the Period
Covering Constraint.................................... 186
6.2.3 The Lagrangean Heuristic for Both Relaxations.......... 187
6.2.3.1 Initial Lagrangean Multiplier................. 189
6.2.3.2 A Lagrangean Heuristic......................... 191
6.3 A More Sophisticated Lagrangean Hybrid Heuristic............. 195
6.3.1 A General Approach to Link Two Lagrangean
Relaxations............................................ 195
6.3.2 The Lagrangean Hybrid Heuristic........................ 201
6.3.2.1 Initial Extended Cover Inequalities........... 202
6.3.2.2 A Hybrid Heuristic............................. 202
6.3.3 Mathematical Formulations of the Auxiliary LPs......... 207
6.3.3.1 The Auxiliary LP DL(c) ....................... 207
6.3.3.2 The Auxiliary LP DL(p)........................ 209
6.4 A Tabu Search Heuristic....................................... 211
6.4.1 The Tabu Search Heuristic.............................. 211
6.4.2 Bitshifting in the Calculation of the Tabu Search
Objective Function..................................... 218
References.......................................................... 221
7 Computations for the Capacitated Planned Maintenance Problem.... 223
7.1 Instance Generation and Test-Sets.............................. 223
7.1.1 A Value for the Mean r0.............................. 224
7.1.2 Test-Sets ............................................ 225
7.2 Absolute Strength of the Lower Bounds.......................... 225
7.3 Performance of the Heuristics.................................. 230
7.3.1 Heuristics to the Lagrangean Relaxations and
Pseudo-Subgradient Optimization........................ 231
7.3.1.1 The Performance of the Heuristics............. 231
7.3.1.2 Applying Different Heuristics in the
Lagrangean Heuristic........................... 233
7.3.1.3 The Approximation of the Lagrangean Duals..... 237
7.3.2 Heuristics to the Planned Maintenance Problem.......... 239
7.3.2.1 The Construction Heuristics.................... 239
7.3.2.2 Variants of the Lagrangean Hybrid Heuristic... 241
7.3.2.3 The Metaheuristics............................. 254
Reference........................................................... 265
8 Final Remarks and Future Perspectives.............................. 267
A Additional Material for the Capacitated Planned
Maintenance Problem............................................... 273
A.l Problem Extensions........................................... 273
A. 1.1 Capacitated Weighted Planned Maintenance Problems... 273
A. 1.2 Multiple Machines.................................... 274
A. 1.3 Multiple Repairmen................................... 274
A. 1.4 Maintenance Precedence Constraints................... 275
A. 1.5 Minimal Time Between Maintenance Activities.......... 275
A. 1.6 Integration with Lot-Sizing.......................... 276
A.2 Mathematical Formulations.................................... 278
References........................................................ 282
Index................................................................ 283
|
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| ctrlnum | (OCoLC)967360375 (DE-599)BVBBV043907366 |
| discipline | Wirtschaftswissenschaften |
| format | Thesis Book |
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| id | DE-604.BV043907366 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:38:11Z |
| institution | BVB |
| isbn | 9783319402888 |
| language | English |
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| physical | xxix, 286 Seiten Diagramme 24 cm |
| publishDate | 2017 |
| publishDateSearch | 2017 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Kuschel, Torben Verfasser (DE-588)1052819419 aut Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties Torben Kuschel [Cham, Schweiz] Springer [2017] xxix, 286 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 686 Dissertation Bergische Universität Wuppertal Includes bibliographical references and index Optimierung (DE-588)4043664-0 gnd rswk-swf Reihenfolgeproblem (DE-588)4242167-6 gnd rswk-swf Instandhaltungsplanung (DE-588)4200074-9 gnd rswk-swf Kapazitätsplanung (DE-588)4120544-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kapazitätsplanung (DE-588)4120544-3 s Instandhaltungsplanung (DE-588)4200074-9 s Reihenfolgeproblem (DE-588)4242167-6 s Optimierung (DE-588)4043664-0 s 1\p DE-604 Lecture notes in economics and mathematical systems 686 (DE-604)BV000000036 686 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=029316486&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 |
| spellingShingle | Kuschel, Torben Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties Lecture notes in economics and mathematical systems Includes bibliographical references and index Optimierung (DE-588)4043664-0 gnd Reihenfolgeproblem (DE-588)4242167-6 gnd Instandhaltungsplanung (DE-588)4200074-9 gnd Kapazitätsplanung (DE-588)4120544-3 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4242167-6 (DE-588)4200074-9 (DE-588)4120544-3 (DE-588)4113937-9 |
| title | Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties |
| title_auth | Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties |
| title_exact_search | Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties |
| title_full | Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties Torben Kuschel |
| title_fullStr | Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties Torben Kuschel |
| title_full_unstemmed | Capacitated planned maintenance models, optimization algorithms, combinatorial and polyhedral properties Torben Kuschel |
| title_short | Capacitated planned maintenance |
| title_sort | capacitated planned maintenance models optimization algorithms combinatorial and polyhedral properties |
| title_sub | models, optimization algorithms, combinatorial and polyhedral properties |
| topic | Optimierung (DE-588)4043664-0 gnd Reihenfolgeproblem (DE-588)4242167-6 gnd Instandhaltungsplanung (DE-588)4200074-9 gnd Kapazitätsplanung (DE-588)4120544-3 gnd |
| topic_facet | Optimierung Reihenfolgeproblem Instandhaltungsplanung Kapazitätsplanung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029316486&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
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