Deterministic scheduling theory:
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| Main Author: | |
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| Format: | Book |
| Language: | Undetermined |
| Published: |
London <<[u.a.]>>
Chapman & Hall
1995
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 290 S. graph. Darst. |
| ISBN: | 0412996812 |
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| 100 | 1 | |a Parker, R. Gary |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Deterministic scheduling theory |c R. Gary Parker |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London <<[u.a.]>> |b Chapman & Hall |c 1995 | |
| 300 | |a XXII, 290 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| adam_text | 1
Contents
List of Figures xi
List of Tables xvii
Preface xix
1 INTRODUCTION 1
1.1 Some Scheduling Problems 2
1.1.1 Bicycle Assembly 2
1.1.2 Classroom Assignment 5
1.1.3 Scheduling Athletic Events 6
1.1.4 Soft Drink Bottling 8
1.2 Classification of Scheduling Problems 9
1.2.1 Machine Environment 11
1.2.2 Job Characteristics 11
1.2.3 Optimality Criteria 12
1.3 Outline of the Book 13
2 MATHEMATICAL PRELIMINARIES 15
2.1 Computational Complexity 15
2.1.1 Problems 17
2.1.2 Computational Orders 17
2.1.3 Problem Size and Encoding 19
2.1.4 Problem Reductions 20
2.1.5 Fundamental Problem Classes 22
2.1.6 What to Do with AfV-Hard (AfV-Complete) Problems 26
2.2 Graph Theory 28
2.2.1 Fundamental Definitions 28
2.2.2 Trees, Forests, Arborescences, and Branchings 31
2.2.3 Covering, Matching, and Independence 31
2.2.4 Vertex Colorings, Edge Colorings, and Perfect Graphs 34
2.3 Partial Enumeration/Branch-and-Bound 36
viii CONTENTS
3 SINGLE-PROCESSOR PROBLEMS 43
3.1 Independent Jobs 43
3.1.1 Completion Time Models 43
3.1.2 Lateness Models 45
3.1.3 Tardiness Models 46
3.2 Dependent Jobs 58
3.2.1 Special Precedence Structures 58
3.2.2 Total Completion Time Models 68
3.2.3 Due-Date Problems 71
3.2.4 Sequence-Dependent Setup Problems 73
3.3 Exercises 75
4 PARALLEL-PROCESSOR PROBLEMS 83
4.1 Independent Jobs 83
4.1.1 Makespan Case 83
4.1.2 Total Completion Time Problems 99
4.2 Dependent Jobs 102
4.2.1 General Precedence 102
4.2.2 Special Precedence Structures 107
4.2.3 The Two-Processor Case 109
4.2.4 Approximations 119
4.3 Exercises 129
5 FLOW SHOPS, JOB SHOPS, AND OPEN SHOPS 135
5.1 Flow Shops 135
5.1.1 Permutation Schedules 136
5.1.2 Solvable Flow Shop Cases 141
5.1.3 General Flow Shops 149
5.2 Job Shops 153
5.2.1 Intra-Job Precedence 154
5.2.2 Inter-Job Precedence 157
5.3 Open Shops 165
5.4 Exercises 171
6 NONSTANDARD SCHEDULING PROBLEMS 177
6.1 The Classroom Assignment Problem 177
6.1.1 Vertex Coloring and the Fundamental Problem 178
6.1.2 Modifications 182
6.2 Staffing Problems 184
6.3 Timetabling Problems 190
6.3.1 Edge-Coloring and Class-1 Graphs 192
6.3.2 Modifications 194
CONTENTS ix
6.4 Exercises 198
! 7 PROJECT SCHEDULING 203
7.1 Project Network Construction 204
7.2 Basic Scheduling Calculations 208
7.2.1 Critical Paths 208
7.2.2 Late Start and Slack Times 210
7.3 Time-Cost Optimization 212
7.3.1 Linear Time-Cost Data 212
7.3.2 Nonstandard Time-Cost Data 220
7.4 Exercises 223
8 CHINESE POSTMEN AND TRAVELING SALESMEN 231
8.1 Eulerian Traversals and the Chinese Postman Problem 231
8.1.1 Eulerian Graphs 232
8.1.2 Postman Problems 235
8.2 Hamiltonian Cycles and the Traveling Salesman Problem 244
8.2.1 Hamiltonian Cycles 245
8.2.2 Heuristics for the Traveling Salesman Problem 250
8.3 Exercises 254
References 259
Index 285
List of Figures
1.1 Bicycle assembly representation 3
1.2 Timing diagram of a task assignment 4
1.3 An improved assembly schedule 4
1.4 An optimal schedule 5
1.5 Representation of event orders for boys and girls 7
1.6 Schedule of girls (resp. boys) first, boys (resp. girls) next 7
1.7 Alternating schedule for girls and boys 8
1.8 An improved schedule 8
2.1 Schedule construction from knapsack solution 22
2.2 Graphs (right) and multigraphs (left) 29
2.3 A sample digraph 29
2.4 Walks, paths, chains, cycles, and circuits 30
2.5 Subgraphs 32
2.6 Regular and complete graphs 33
2.7 Isomorphism and homeomorphism 34
2.8 Trees and arborescences 35
2.9 Covers, independent sets, matchings, and cliques 35
2.10 Colorings in graphs 37
2.11 Branch-and-bound tree for Example 2.2 41
3.1 Bipartite graph of Example 3.4 49
3.2 Sense of ordering from Theorem 3.12 51
3.3 EDD ordering in Example 3.6 53
3.4 Outcome of iteration 2 in Example 3.6 54
3.5 Final schedule for Example 3.7 57
3.6 Precedence chains 59
3.7 In/out forests/trees 60
3.8 Construction of a vertex transitive series-parallel graph 61
3.9 A vertex series-parallel digraph 62
3.10 A digraph that is not vertex series-parallel 62
Xii LIST OF FIGURES
3.11 Forbidden subgraph recognition 63
3.12 Decomposition tree for graph of Figure 3.9 64
3.13 Two decomposition trees of the same graph 64
3.14 Edge series-parallel decomposition 66
3.15 Forbidden subgraph of 2-terminal, edge series-parallel digraphs 66
3.16 Line graph construction 67
3.17 Relationship between forbidden graphs 68
3.18 Vertex series-parallel graph and its decomposition tree 70
3.19 Final sequence 71
3.20 A suitable schedule from a clique of size k 72
3.21 Graph of Example 3.11 73
3.22 Timing diagram relative to an instance of l seq.dep. Cmax 74
3.23 Exercise 3-13 77
3.24 Exercise 3-19 78
3.25 Exercise 3-20 78
3.26 Exercise 3-25 79
3.27 Exercise 3-26 80
3.28 Exercise 3-28 80
4.1 Timing diagram of Example 4.1 84
4.2 Timing diagram of Example 4.2 85
4.3 Bad instance for Akk with k = 0 87
4.4 Schedule generated by L(k) 87
4.5 An optimal schedule 88
4.6 An LPT schedule 89
4.7 LPT for k = 2m - n 90
4.8 Suboptimality of LPT with n = 2m 91
4.9 Parallel-processor scheduling -*• bin-packing 92
4.10 Affd application 93
4.11 Schedule generated for Example 4.7 94
4.12 Affd anomaly 95
4.13 Anomaly-proof target capacity C 95
4.14 Bound on r2 96
4.15 Bound on r3 97
4.16 Bound in rm, m 4 97
4.17 Schedule for instance of R Hcj 100
4.18 Graph of Example 4.9 101
4.19 Construction of Theorem 4.10 104
4.20 A suitable schedule with Cmax = 3 105
4.21 Sample reduction from Theorem 4.10 106
4.22 Digraph for Example 4.11 108
4.23 Digraph on which Ah fails 109
LIST OF FIGURES xiii
| 4.24 Graph of Example 4.13 111
] 4.25 Instance of Example 4.14 113
4.26 Non-transitively reduced graph 114
4.27 Acg failure when m = 3 115
4.28 Application of AGj 119
4.29 Bicycle assembly graph 120
4.30 Effect of increasing m from 3 to 2 120
4.31 List-processing generated schedule 121
4.32 Worst-case sense of Theorem 4.20 bound 123
4.33 Worst-case arborescences 124
4.34 Insufficiency of optimality and robust schedules 125
4.35 Schedules generated from instance of Figure 4.34 126
4.36 Optimal/suboptimal m + l m processor schedules 126
4.37 Schedules of Example 4.20 127
4.38 Tovey s construction 127
4.39 Four to three-processor schedules for Example 4.21 128
4.40 Three to four-processor schedules for Example 4.21 128
4.41 Exercise 4-9 130
4.42 Exercise 4-12 130
4.43 Exercise 4-24 132
4.44 Exercise 4-35 133
4.45 Exercise 4-36 133
4.46 Exercise 4-37 134
5.1 Flow shop structure 136
5.2 Flow shop solution/schedule 137
5.3 Properties Pi and P2 138
5.4 P2 does not hold for Eci 139
5.5 Permutation solutions are not sufficient with m 4 140
5.6 Jobs i and j are initial jobs 141
5.7 Jobs i and j are not initial jobs 142
5.8 Example 5.1 143
5.9 Demonstration of property Pi 145
5.10 Example 5.4 148
5.11 Primative branch-and-bound tree for flow shops 150
5.12 Concept of B%(SP) 151
5.13 Tree for Example 5.7 152
5.14 Job shop structure 154
5.15 J2||Cmax structure for proof of Theorem 5.7 155
5.16 Relationship between a suitable schedule and a knapsack
solution 156
5.17 Example 5.9 157
xiv LIST OF FIGURES
5.18 Nonactive and active schedules 158
5.19 General job shop structure 159
5.20 Example 5.10 161
5.21 Tree of active schedules for Example 5.10 161
5.22 Example 5.11 163
5.23 Reference Example 5.12 164
5.24 Open shop illustration 166
5.25 Concept of proof of Theorem 5.12 167
5.26 Final schedule for Example 5.13 168
5.27 Example 5.14 171
5.28 Matchings of Example 5.14 172
5.29 Schedule construction of Example 5.14 173
5.30 Exercise 5-4 174
5.31 Exercise 5-15 175
5.32 Exercise 5-16 175
6.1 Graph of Earth Day illustration 179
6.2 Sample construction of Theorem 6.1 180
6.3 Schedule generated from the coloring of Example 6.1 181
6.4 Staffing of Example 6.2 186
6.5 Staffing of Example 6.3 187
6.6 Constraint matrices of Example 6.4 189
6.7 Row circularity determination 191
6.8 Timetable for Example 6.5 192
6.9 Sample graph formed from R 193
6.10 Disjoint matchings of graph in Figure 6.9 194
6.11 Construction of Lemma 6.9 196
7.1 AOA depiction of the bicycle assembly requirements 205
7.2 Alterative dummy activity use 206
7.3 Illustration of the construction of Theorem 7.1 207
7.4 AOA network of example 210
7.5 Time-cost illustration 214
7.6 Compressions for Example 7.6 214
7.7 Arc computations for Example 7.7 218
7.8 Modified network structure for the case 0 /y Sy 219
7.9 Pseudo-activity construction 221
7.10 Nonconvex time-cost functions 222
7.11 Discrete time-cost data 223
7.12 Exercise 7-2 224
7.13 Exercise 7-4 224
7.14 Exercise 7-5 225
I
LIST OF FIGURES xv
7.15 Exercise 7-7 225
7.16 Exercise 7-12 226
7.17 Exercise 7-13 227
7.18 Exercise 7-18 228
7.19 Exercise 7-20 228
7.20 Exercise 7-21 229
8.1 Eulerian and non-Eulerian graphs 232
8.2 Directed Eulerian traversal 234
8.3 Eulerian traversal in a mixed graph 235
8.4 PSym solution for a mixed graph 236
8.5 Graphs of Example 8.3 237
8.6 Digraph of Example 8.4 239
8.7 Postman construction for mixed graphs 240
8.8 Application of Aes 241
8.9 Application of ASe 242
8.10 Behavior of AES and ASe 243
8.11 Worst-known graph for the composite use of Aes and A $e 244
8.12 A non-Hamiltonian graph 246
8.13 Graphs of Example 8.7 247
8.14 Non-Hamiltonian graph generated by Chvatal s construction
procedure 248
8.15 Graph of Example 8.8 249
8.16 Application of algorithm Ac 251
8.17 Relationship between Vo vertices and a tour 252
8.18 Worst-case instance for Ac 253
8.19 Step 1 construction 253
8.20 Step 2 construction 253
8.21 Exercise 8-1 254
8.22 Exercise 8-2 255
8.23 Exercise 8-4 255
8.24 Exercise 8-5 256
8.25 Exercise 8-9 257
List of Tables
3.1 Computation for Example 3.11 74
7.1 Example 7.4 211
7.2 Modified Network Construction 217
7.3 Capacity specification in the maximum flow network 217
|
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| author | Parker, R. Gary |
| author_facet | Parker, R. Gary |
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| bvnumber | BV024419551 |
| ctrlnum | (OCoLC)832651836 (DE-599)BVBBV024419551 |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
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| dewey-search | 658.53 |
| dewey-sort | 3658.53 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Wirtschaftswissenschaften |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV024419551 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:59:13Z |
| institution | BVB |
| isbn | 0412996812 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018397185 |
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| physical | XXII, 290 S. graph. Darst. |
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| publisher | Chapman & Hall |
| record_format | marc |
| spelling | Parker, R. Gary Verfasser aut Deterministic scheduling theory R. Gary Parker 1. ed. London <<[u.a.]>> Chapman & Hall 1995 XXII, 290 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Reihenfolgeproblem (DE-588)4242167-6 gnd rswk-swf Tourenplanung (DE-588)4121783-4 gnd rswk-swf Reihenfolgeproblem (DE-588)4242167-6 s DE-188 Tourenplanung (DE-588)4121783-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018397185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parker, R. Gary Deterministic scheduling theory Reihenfolgeproblem (DE-588)4242167-6 gnd Tourenplanung (DE-588)4121783-4 gnd |
| subject_GND | (DE-588)4242167-6 (DE-588)4121783-4 |
| title | Deterministic scheduling theory |
| title_auth | Deterministic scheduling theory |
| title_exact_search | Deterministic scheduling theory |
| title_full | Deterministic scheduling theory R. Gary Parker |
| title_fullStr | Deterministic scheduling theory R. Gary Parker |
| title_full_unstemmed | Deterministic scheduling theory R. Gary Parker |
| title_short | Deterministic scheduling theory |
| title_sort | deterministic scheduling theory |
| topic | Reihenfolgeproblem (DE-588)4242167-6 gnd Tourenplanung (DE-588)4121783-4 gnd |
| topic_facet | Reihenfolgeproblem Tourenplanung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018397185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT parkerrgary deterministicschedulingtheory |