Claude Le Pape

Constraint-Based Job Shop Scheduling with {\sc Ilog\ Scheduler}

We introduce constraint-based scheduling and discuss its main principles. An approximation algorithm based on tree search is developed for the job shop scheduling problem using ILOG SCHEDULER. A new way of calculating lower bounds on the makespan of the job shop scheduling problem is presented and we show how such results can be used within a constraint-based approach. An empirical performance analysis shows that the algorithm we developed performs well. Finally, taking the job shop scheduling problem as a start point, we discuss how constraint-based scheduling can be used to solve more general scheduling problems.

Global Constraints for Partial CSPs: A Case-Study of Resource and Due Date Constraints

This paper presents the results of a case study, concerning the propagation of a global disjunctive resource constraint, when the resource is over-loaded. The problem can be seen as a partial constraint satisfaction problem, in which either the resource constraint or the due dates of some jobs have to be violated. Global constraint propagation methods are introduced to efficiently deal with this situation. These methods are applied to a well-known operations research problem: minimizing the number of late jobs on a single machine, when jobs are subjected to release dates and due dates. Dominance criteria and a branch and bound procedure are developed for this problem. 960 instances are generated with respect to different characteristics (number of jobs, overload ratio, distribution of release dates, of due dates and of processing times). Instances with 60 jobs are solved in 23 seconds on average and 90% of the instances with 100 jobs are solved in less than 1 hour.

Constraint-based scheduling and planning

Publisher Summary This chapter describes constraint-based scheduling as the discipline that studies how to solve scheduling problems by using constraint programming (CP). Constraint-based planning in turn is the discipline that studies how to solve planning problems by CP. The chapter discusses that constraint-based scheduling is one of the most successful application areas of CP. One of the key factors of this success lies in the fact that a combination was found of the best of two fields of research that pay attention to scheduling—namely, operations research (OR) and artificial intelligence (AI). The chapter reviews that OR approach aims at achieving a high level of efficiency in its algorithms whereas AI research tends to investigate more general scheduling models and tries to solve the problems by using general problem-solving paradigms. The use of CP in planning is because of the problem complexity, which is less mature than its use in scheduling. Constraint-based planning thus follows the same pattern as constraint-based scheduling where CP is used as a framework for integrating efficient special purpose algorithms into a flexible and expressive paradigm. It also presents CP models for scheduling together with descriptions of propagation techniques for constraints used in these models.

Constraint Propagation and Decomposition Techniques forHighly Disjunctive and Highly Cumulative Project Scheduling Problems

In recent years, constraint satisfaction techniques have been successfully applied to “disjunctive” scheduling problems, i.e., scheduling problems where each resource can execute at most one activity at a time. Less significant and less generally applicable results have been obtained in the area of “cumulative” scheduling. Multiple constraint propagation algorithms have been developed for cumulative resources but they tend to be less uniformly effective than their disjunctive counterparts. Different problems in the cumulative scheduling class seem to have different characteristics that make them either easy or hard to solve with a given technique. The aim of this paper is to investigate one particular dimension along which problems differ. Within the cumulative scheduling class, we distinguish between “highly disjunctive” and “highly cumulative” problems: a problem is highly disjunctive when many pairs of activities cannot execute in parallel, e.g., because many activities require more than half of the capacity of a resource; on the contrary, a problem is highly cumulative if many activities can effectively execute in parallel. New constraint propagation and problem decomposition techniques are introduced with this distinction in mind. This includes an O(n2) “edge-finding” algorithm for cumulative resources (where n is the number of activities requiring the same resource) and a problem decomposition scheme which applies well to highly disjunctive project scheduling problems. Experimental results confirm that the impact of these techniques varies from highly disjunctive to highly cumulative problems. In the end, we also propose a refined version of the “edge-finding” algorithm for cumulative resources which, despite its worst case complexity in O(n3) , performs very well on highly cumulative instances.

Heuristic Control of a Constraint-Based Algorithm for the Preemptive Job-Shop Scheduling Problem

In the recent years, constraint programming has been applied to a wide variety of academic and industrial non-preemptive scheduling problems, i.e., problems in which activities cannot be interrupted. In comparison, preemptive scheduling problems have received almost no attention from both the Operations Research and the Artificial Intelligence community. Motivated by the needs of a specific application, we engaged in a study of the applicability of constraint programming techniques to preemptive scheduling problems. This paper presents the algorithms we developed and the results we obtained on the preemptive variant of the famous “job-shop scheduling problem.” Ten heuristic search strategies, combined with two different constraint propagation techniques, are presented, and compared using two well-known series of job-shop scheduling instances from the literature. The best combination, which relies on “limited discrepancy search” and on “edge-finding” techniques, is shown to provide excellent solutions to the preemptive job-shop scheduling problem. A mean relative distance to the optimal solution of 0.32% is achieved in five minutes, on instances with 10 jobs and 10 machines (100 activities).

Resource Constraints for Preemptive Job-shop Scheduling

This paper presents an experimental study of constraint propagation algorithms for preemptive scheduling. We propose generalizations of non-preemptive constraint propagation techniques (based on timetables, on disjunctive constraints, and on edge-finding) to preemptive and “mixed” problems, i.e., problems in which some activities can be interrupted and some cannot. Another approach relies on incremental flow-based techniques. We theoretically compare these approaches and present an experimental comparison based on a branch and bound procedure for the preemptive variant of the job-shop scheduling problem. We show that both edge-finding and flow-based techniques allow the resolution of hard problem instances, including the preemptive variant of the famous FT10.