Scheduling of Resource-Constrained Projects

378 Pages·2000·9.686 MB·English

by  Robert Klein (auth.)

Scheduling of
Resource-Constrained Projects
OPERATIONS RESEARCH/COMPUTER SCIENCE
INTERFACES SERIES
Series Editors
Professor Ramesh Sharda Prof. Dr. Stefan VoB
Oklahoma State University Technische Universitdt Braunschweig
Other published titles in the series:
Brown, Donald/Scherer, William T.
Intelligent Scheduling Systems
Nash, Stephen G.lSofer, Ariela
The Impact of Emerging Technologies on Computer Science
and Operations Research
Barth, Peter
Logic-Based 0-1 Constraint Programming
Jones, Christopher V.
Visualization and Optimization
Barr, Richard S.I Helgason, Richard V.I Kennington, Jeffery L.
Interfaces in Computer Science and Operations Research: Advances in
Metaheuristics, Optimization, and Stochastic Modeling Technologies
Ellacott, Stephen W.I Mason, John C.I Anderson, lain J.
Mathematics of Neural Networks: Models, Algorithms & Applications
Woodruff, David L.
Advances in Computational and Stochastic Optimization, Logic
Programming, and Heuristic Search
Scheduling of
Resource-Constrained Projects
by
Robert Klein
~.
"
Springer-Science+ Business Media, LLC
Library of Congress Cataloging-in-Publication
Klein, Robert.
Scheduling of resource-constrained projects / by Robert Klein.
p.cm. --(Operations research/ computer science interfaces series ; OReS 10)
Includes bibIiographical references and index.
ISBN 978-1-4613-7093-2 ISBN 978-1-4615-4629-0 (eBook)
DOI 10.1007/978-1-4615-4629-0
1. Production scheduIing. 1. TitIe. II. Series.
TSI57.5.K5541999
658.5'3--dc21
99-046684
e
Copyright 2000 by Springer Science+Business Media New York
Origina1ly published by Kluwer Academic Publishers in 2000
Softcover reprint of the hardcover 1s t edition 2000
AlI rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, record ing, or otherwise, without the prior written permission of the
publisher, Springer-Science+Business Media, LLC.
Printed on acid-free paper.
Contents
Notations................................................................................................... XI
Preface ..................................................................................................... XV
Part I Project Management: Basics and Scheduling Problems
1 The Project Management Process............................................................. 1
1.1 Definition ofa Project .......................................................................................... .
1.2 The Project Life Cycle .......................................................................................... 2
1.3 Project Conception ................................................................................................ 5
1.3.1 Feasibility Study ............................................................................................ 7
1.3.2 Economic Analysis ........................................................................................ 8
1.3.3 Risk Analysis ............................................................................................... 10
1.3.4 Project Selection .......................................................................................... 12
1.4 Project Definition ................................................................................................ 15
1.4.1 Project Specification .................................................................................... IS
1.4.2 Project Organization .................................................................................... 16
1.4.3 Process Organization.......... ...... ............................ ...................... ................. 17
1.4.4 Budgeting..................................................................................................... 19
1.5 Project Planning .................................................................................................. 22
1.5.1 Structuring ................................................................................................... 22
1.5.2 Scheduling ................................................................................................... 24
1.5.3 Resource Allocation .................................................................................... 24
1.6 Project Execution ................................................................................................ 26
1.6.1 Reporting, Monitoring, and Control............................................................ 27
1.6.2 Configuration Management ......................................................................... 28
1.6.3 Quality Management ................................................................................... 29
VI Contents
1.7 Project Termination ............................................................................................ 30
1.7.1 Final Evaluation and Reporting ................................................................... 30
1.7.2 Dissolution ................................................................................................... 31
2 Project Planning and Control.................................................................. 33
2.1 Structuring ........................................................................................................... 34
2.1.1 Work Breakdown Structure ......................................................................... 34
2.1.2 Activity-on-Node Networks ........................................................................ 37
2.1.3 Activity-on-Arc Networks ........................................................................... 41
2.2 Scheduling ............................................................................................................ 43
2.2.1 Critical Path Analysis ................................................ .................................. 43
2.2.2 Slack Time Computations .................. ......................................................... 46
2.2.3 Gantt Charts ................................................................................................. 49
2.3 Resource Allocation ............................................................................................ 50
2.3.1 Resource Loading ........................................................................................ 50
2.3.2 Resource-Constrained Scheduling............................................................... 52
2.3.3 Time-Constrained Scheduling ..................................................................... 54
2.4 Control ................................................................................................................. 55
2.4.1 Schedule Control.. .............. ...................... .......... ............. ............................ 56
2.4.2 Cost Control ................................................................................................. 60
2.5 Project Management Software .......................................................................... 63
2.5.1 Features for Project Conception, Definition, and Termination ................... 64
2.5.2 Features for Project Planning ...................................................................... 65
2.5.3 Features for Project Execution .................................................................... 68
2.5.4 General Features .......................................................................................... 70
3 Resource-Constrained Scheduling Problems......................................... 73
3.1 Notations and Definitions ................................................................................... 73
3.2 Basic Models ........................................................................................................ 76
3.2.1 The Resource-Constrained Project Scheduling Problem (RCPSP) ............. 77
3.2.1.1 Properties ofRCPSP ..................................................................... 77
3.2.1.2 Formulation I ................................................................................ 79
3.2.1.3 Formulation 2 ................................................................................ 80
3.2.1.4 Formulation 3 ................................................................................ 82
3.2.1.5 Formulation 4 ................................................................................ 84
3.2.1.6 Formulation 5 ................................................................................ 86
3.2.1.7 Formulation 6 ................................................................................ 87
Contents VII
3.2.2 The Generalized Resource-Constrained Project Scheduling Problem ....... 89
3.2.2.1 Properties ofGRCPSP ................................................................... 91
3.2.2.2 Formulations.................................................................................. 92
3.2.3 Problem Complexity .................................................................................... 92
3.3 Extensions of the Basic Models .......................................................................... 95
3.3.1 Preemption ................................................................................................... 96
3.3.2 Multiple Modes ............................................................................................ 96
3.3.3 Maximum Time Lags .................................................................................. 99
3.3.4 State Preserving Jobs .................................................................... ............. 100
3.3.5 Further Extensions ..................................................................................... 102
3.4 Related Project Scheduling Problems ............................................................. 102
3.4.1 The Time-Constrained Project Scheduling Problem ................................. 103
3.4.2 The Resource Leveling Problem ............................................................... 104
3.4.3 The Resource Investment Problem ............................................................ 105
3.4.4 The Net Present Value Problem ................................................................ 106
3.4.5 The Weighted Tardiness Problem ............................................................. 108
3.4.6 Further Resource-Constrained Project Scheduling Problems ................... 108
Part II Resource-Constrained Project Scheduling:
Solution Methods
4 Lower Bound Methods........................................................................... 113
4.1 Constructive Lower Bound Methods for RCPSP .......................................... 114
4.1.1 Simple Bound Arguments ......................................................................... 114
4.1.1.1 Critical Path and Capacity Bounds .............................................. 114
4.1.1.2 Bin Packing Bounds .................................................................... 117
4.1.1.3 Node Packing Bounds ................................................................. 120
4.1.1.4 Parallel Machine Bounds......... ........ ...... ................... ................... 124
4.1.1.5 Precedence Bounds.. ....................................... ............................. 128
4.1.2 Complex Bound Arguments ........ ................ ........................................... ... 129
4.1.2.1 LP-Relaxation with Cutting Planes ............................................. 130
4.1.2.2 Lagrangean Relaxation ................................................................ 132
4.1.2.3 Set Covering Based Approach .. .............. ..... ...... .......... .......... ..... 134
4.2 Destructive Improvement................................................................................. 136
4.2.1 Meta-Strategies for Computing Lower Bounds......................................... 136
4.2.2 Applying Destructive Improvement to RCPSP ................................ ......... 141
4.2.2.1 Reduction Techniques ................................................................. 141
4.2.2.2 Lower Bound Arguments for Contradicting Feasibility .............. 147
VIII Contents
4.3 Lower Bound Methods for GRCPSP .............................................................. 149
4.3.1 Simple Bound Arguments ......................................................................... 150
4.3.1.1 Critical Path and Capacity Bounds.............................................. 152
4.3.1.2 Node Packing Bounds ................................................................. 153
4.3.1.3 Parallel Machine Bounds............................................................. 157
4.3.1.4 Precedence Based Bounds........................................................... 158
4.3.2 Destructive Improvement .......................................................................... 159
5 Heuristic Procedures .............................................................................. 161
5.1 Types of Schedules ............................................................................................ 162
5.2 Priority-Rule Based Methods ........................................................................... 167
5.2.1 Scheduling Schemes .................................................................................. 169
5.2.1.1 Serial Scheduling Scheme ........................................................... 169
5.2.1.2 Parallel Scheduling Scheme ........................................................ 171
5.2.1.3 A Critique of the Scheduling Schemes........................................ 173
5.2.2 Multiple Planning Directions..................................................................... 175
5.2.2.1 Backward Planning ...................................................................... 175
5.2.2.2 Bidirectional Planning ................................................................. 178
5.2.3 Priority Rules ............................................................................................. 181
5.2.4 Multi-Pass Priority-Rule Based Heuristics................................................ 187
5.3 Improvement Methods ..................................................................................... 190
5.3.1 The Meta-Heuristic Tabu Search ............................................................... 191
5.3.1.1 Moves, Neighborhood, and Descent Procedures......................... 191
5.3.1.2 Basic Principles of Tabu Search.................................................. 193
5.3.1.3 Extensions of the Basic Approach............................................... 196
5.3.2 The Tabu Search Procedure RETAPS ......................................................... 198
5.3.2.1 Definition of the Neighborhood .................................................. 198
5.3.2.2 Tabu Management and Diversification ....................................... 204
5.3.3 Other Meta-Heuristic Based Procedures for RCPSP ................................. 208
6 Exact Procedures .................................................................................... 213
6.1 Components of Branch and Bound Procedures ............................................. 214
6.1.1 Branching Schemes .......... ............................................................. .... ........ 215
6.1.2 Search Strategies....................... ........................................................... ...... 216
6.1.3 Bounding Rules ........................................................................... .............. 218
6.1.4 Reduction Rules ......................................................................................... 219
6.1.5 Dominance Rules ....................................................................................... 220
Contents IX
6.2 The Branch and Bound Procedure PROGRESS ...........................................•... 221
6.2.1 The Branching Scheme.............................................................................. 222
6.2.2 Local Lower Bound Method...................................................................... 224
6.2.3 Bounding Rules ......................................................................................... 226
6.2.4 Reduction and Dominance Rules .............................................................. 228
6.2.4.1 Core Time Rule ........................................................................... 228
6.2.4.2 Active Schedule Rules................................................................. 229
6.2.4.3 Supersession Rule........................................................................ 231
6.2.4.4 Schedule Storing Rules .................................. ............................. 232
6.2.5 Example ..................................................................................................... 236
6.3 Scattered Branch and Bound ............................•.............................................. 240
6.3.1 Principles ofScauered Branch and Bound ................................................ 241
6.3.1.1 A Critique of Traditional Branch and Bound .............................. 241
6.3.1.2 Subdividing the Solution Space into Regions ............................. 243
6.3.1.3 Swapping Regions ....................................................................... 245
6.3.2 SCATTER: Scattered Branch and Bound for GRCPSP ............................... 247
6.3.2.1 Outline ......................................................................................... 247
6.3.2.2 Decomposing the Solution Space ................................................ 248
6.3.2.3 Swapping Regions ....................................................................... 249
6.3.2.4 Example ....................................................................................... 251
6.4 Existing Procedures .......................................................................................... 252
6.4.1 Parallel Branching Scheme........................................................................ 253
6.4.2 Serial Branching Scheme..... ............ .......................................................... 254
6.4.3 Delaying Alternatives ................................................................................ 256
6.4.4 Schedule Schemes ..................................................................................... 258
7 Computational Experiments ................................................................. 261
7.1 Hardware and Software Environment.. .......................................................... 262
7.2 Complexity Measures and Data Sets ............................................................... 263
7.2.1 Complexity Measures ................................................................................ 263
7.2.2 Data Sets for RCPSP ................................................................................. 267
7.2.3 Data Sets for GRCPSP .............................................................................. 269
7.3 Lower Bound Arguments ................................................................................. 274
7.3.1 Simple Bound Arguments ......................................................................... 275
7.3.2 Destructive Improvement .......................................................................... 278
7.3.3 Influence of the Problem Structure ............................................................ 281
7.3.4 Comparison with Complex Bound Arguments ......................................... 284
X Contents
7.4 Heuristic Procedures ......................................................................................... 286
7.4.1 Priority-Rule Based Heuristics .................................................................. 286
7.4.1.1 Combinations of Scheduling Schemes and Priority Rules .......... 287
7.4.1.2 Influence of the Problem Structure .............................................. 290
7.4.1.3 Multi-Pass Performance .............................................................. 293
7.4.1.4 Comparison to Proprietary Heuristics of Standard Software ...... 295
7.4.1.5 Results for GRCPSP .................................................................... 296
7.4.2 The Tabu Search Procedure RETAPS ......................................................... 300
7.4.2.1 Analysis of GRCPSP Performance ............................................. 301
7.4.2.2 Comparing RETAPS to Multi-Pass Heuristics .............................. 304
7.4.2.3 Comparing RETAPS to Other Heuristic Procedures for RCPSP .. 305
7.5 Exact Procedures ............................................................................................... 306
7.5.1 The Branch and Bound Procedure PROGRESS ........................................... 306
7.5.1.1 Comparing PROGRESS to GOH ..................................................... 307
7.5.1.2 Analyzing the Efficiency of PROGRESS ....................................... 309
7.5.2 Scattered Branch and Bound ..................................................................... 313
7.5.2.1 Comparing SCATTER to PROGRESS .............................................. 313
7.5.2.2 Comparing SCATTER to Existing RCPSP Procedures ................. 318
7.5.2.3 Comparing SCATTER to RETAPS .................................................. 321
8 Summary and Conclusions .................................................................... 325
References ............................................................................................... 333
Index ........................................................................................................ 365