Constraint-Based Scheduling

Applying Constraint Programming to Scheduling Problems

By: Philippe Baptiste, Claude Le Pape, Wim Nuijten

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Hardcover | 31 July 2001

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220 Pages

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Constraint Programming is a problem-solving paradigm that establishes a clear distinction between two pivotal aspects of a problem: (1) a precise definition of the constraints that define the problem to be solved and (2) the algorithms and heuristics enabling the selection of decisions to solve the problem.
It is because of these capabilities that Constraint Programming is increasingly being employed as a problem-solving tool to solve scheduling problems. Hence the development of Constraint-Based Scheduling as a field of study.
The aim of this book is to provide an overview of the most widely used Constraint-Based Scheduling techniques. Following the principles of Constraint Programming, the book consists of three distinct parts:

The first chapter introduces the basic principles of Constraint Programming and provides a model of the constraints that are the most often encountered in scheduling problems.
Chapters 2, 3, 4, and 5 are focused on the propagation of resource constraints, which usually are responsible for the "hardness" of the scheduling problem.
Chapters 6, 7, and 8 are dedicated to the resolution of several scheduling problems. These examples illustrate the use and the practical efficiency of the constraint propagation methods of the previous chapters. They also show that besides constraint propagation, the exploration of the search space must be carefully designed, taking into account specific properties of the considered problem (e.g., dominance relations, symmetries, possible use of decomposition rules).

Chapter 9 mentions various extensions of the model and presents promising research directions.

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Paperback

Published: 26th October 2012

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Foreword	p. ix
Preface	p. xi
Acknowledgments	p. xiii
Introduction	p. 1
Introduction to Constraint Programming	p. 1
Scheduling Theory	p. 9
Graham's Classification	p. 10
A Constraint-Based Scheduling Model	p. 12
Activities	p. 12
Temporal Relations	p. 15
Resource Constraints	p. 15
Extensions of the Model	p. 16
Objective Function	p. 18
Propagation of the One-Machine Resource Constraint	p. 19
Non-Preemptive Problems	p. 19
Time-Table Constraint	p. 19
Disjunctive Constraint Propagation	p. 21
Edge-Finding	p. 22
Not-First, Not-Last	p. 26
More Propagation	p. 29
Preemptive Problems	p. 31
Time-Table Constraint	p. 32
Disjunctive Constraint Propagation	p. 33
Network-Flow Based Constraints	p. 33
Preemptive Edge-Finding	p. 37
Propagation of Cumulative Constraints	p. 43
Fully Elastic Problems	p. 44
Preemptive Problems	p. 46
Time-Table Constraint	p. 46
Disjunctive Constraint	p. 46
Partially Elastic Relaxation	p. 46
Non-Preemptive Problems	p. 58
Time-Table Constraint	p. 58
Disjunctive Constraint	p. 59
Edge-Finding	p. 59
Extended Edge-Finding	p. 64
Not-First, Not-Last	p. 65
Energetic Reasoning	p. 67
Comparison of Propagation Techniques	p. 77
Constraint Propagation Rules	p. 77
Time-Table Constraints	p. 80
Disjunctive Constraints	p. 81
Edge-Finding	p. 81
Not-First, Not-Last	p. 83
Energetic Reasoning	p. 83
Dominance Relations	p. 85
The Fully Elastic Case	p. 87
The Cumulative Preemptive Case	p. 87
The One-Machine Preemptive Case	p. 87
The Cumulative Non-Preemptive Case	p. 88
The One-Machine Non-Preemptive Case	p. 91
Non-Dominance Relations	p. 92
General Counterexamples	p. 93
A One-Machine Preemptive Counterexample	p. 96
Cumulative Counterexamples	p. 96
Summary	p. 99
The Fully Elastic Case	p. 99
The Cumulative Preemptive Case	p. 100
The One-Machine Preemptive Case	p. 100
The Cumulative Non-Preemptive Case	p. 100
The One-Machine Non-Preemptive Case	p. 101
Propagation of Objective Functions	p. 105
Total Weighted Number of Late Activities	p. 105
Complexity Results	p. 106
A Lower Bound of the Number of Late Activities	p. 108
Constraint Propagation	p. 117
Sum of Transition Times and Sum of Transition Costs	p. 122
Route Optimization Constraint	p. 124
Precedence Graph Constraint	p. 126
Conclusion	p. 127
Resolution of Disjunctive Problems	p. 129
Job-Shop Scheduling	p. 129
Branching Scheme	p. 130
Computational Results	p. 131
Open-Shop Scheduling	p. 132
Branching Scheme	p. 132
More and More Propagation: Shaving	p. 132
Computational Results	p. 133
Conclusion	p. 134
Preemptive Job-Shop Scheduling	p. 135
Dominance Relation	p. 136
Branching Scheme	p. 138
Heuristic Algorithms	p. 140
Limited Discrepancy Search	p. 142
Cumulative Scheduling Problems	p. 149
General Framework	p. 151
Hybrid Flow-Shop Scheduling	p. 154
Resource-Constrained Project Scheduling	p. 155
Conclusion	p. 156
Min-Sum Scheduling Problems	p. 159
Minimizing the Weighted Number of Late Jobs	p. 159
Dominance Relations	p. 160
Branching Scheme	p. 163
Computational Results	p. 164
Minimizing Makespan and Sum of Transition Times	p. 166
Problem Definition	p. 166
Problem Solving	p. 167
Computational Results	p. 169
Conclusion	p. 175
Summary of Notation	p. 179
References	p. 183
Index	p. 197
Table of Contents provided by Syndetics. All Rights Reserved.

Constraint-Based Scheduling

Applying Constraint Programming to Scheduling Problems

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