A Theoretical and Experimental Comparison of Constraint Propagation Techniques for Disjunctive Scheduling

Abstract

Disjunctive constraints are widely used to ensure that the time intervals over whichtwo activities require the same resource cannot overlap: if a resource is required bytwo activities A and B, the disjunctive constraint states that either A precedes B or B precedes A. The #propagation " of disjunctive constraints consists in determining cases where only one of the two orderings is feasible. It results in updating the time-bounds of the two activities. The standard algorithm for propagating disjunctive constraints achieves arc-B-consistency. Twotypes of methods that provide more precise timebounds are studied and compared. The #rst type of method consists in determining whether an activity A must, can, or cannot be the #rst or the last to execute among a set of activities that require the same resource. The second consists in comparing the amount of #resource energy" required over a time interval #t 1 t 2 #to the amount of energy that is available over the same interval. The main result of the study is an implementation of the #rst method in Ilog Schedule, a generic tool for constraint-based scheduling which exhibits performance in the same range of e#ciency as speci#c operations research algorithms.