Constraint-Based Scheduling

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.

Inhalt

1. Introduction.- 1.1 Introduction to Constraint Programming.- 1.2 Scheduling Theory.- 1.3 A Constraint-Based Scheduling Model.- 2. Propagation of the One-Machine Resource Constraint.- 2.1 Non-Preemptive Problems.- 2.2 Preemptive Problems.- 3. Propagation of Cumulative Constraints.- 3.1 Fully Elastic Problems.- 3.2 Preemptive Problems.- 3.3 Non-Preemptive Problems.- 4. Comparison of Propagation Techniques.- 4.1 Constraint Propagation Rules.- 4.2 Dominance Relations.- 4.3 Non-Dominance Relations.- 4.4 Summary.- 5. Propagation of Objective Functions.- 5.1 Total Weighted Number of Late Activities.- 5.2 Sum of Transition Times and Sum of Transition Costs.- 5.3 Conclusion.- 6. Resolution of Disjunctive Problems.- 6.1 Job-Shop Scheduling.- 6.2 Open-Shop Scheduling.- 6.3 Preemptive Job-Shop Scheduling.- 7. Cumulative Scheduling Problems.- 7.1 General Framework.- 7.2 Hybrid Flow-Shop Scheduling.- 7.3 Resource-Constrained Project Scheduling.- 7.4 Conclusion.- 8. Min-Sum Scheduling Problems.- 8.1 Minimizing the Weighted Number of Late Jobs.- 8.2 Minimizing Makespan and Sum of Transition Times.- 9. Conclusion.- 10. Summary of Notation.- References.