Global constraints for partial CSPs: A case-study of resource and due date constraints

Abstract

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.