An algorithm for solving the job-shop problem
Management Science
A practical use of Jackson's preemptive schedule for solving the job shop problem
Annals of Operations Research
A branch and bound algorithm for the job-shop scheduling problem
Discrete Applied Mathematics - Special volume: viewpoints on optimization
Nearly on line scheduling of preemptive independent tasks
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Why cumulative decomposition is not as bad as it sounds
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Explaining the cumulative propagator
Constraints
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The aim of this paper is to show the usefulness of the Jackson's pseudo-preemptive schedule (JPPS) for solving cumulative scheduling problems. JPPS was introduced for the m-processor scheduling problem Pm/ri, qi/Cmax. In the latter problem, a set I of n operations has to be scheduled without preemption on m identical processors in order to minimize the makespan. Each operation i has a release date (or head) ri, a processing time pi, and a tail qi. In the cumulative scheduling problem (CuSP), an operation i requires a constant amount ei of processors throughout its processing. A CuSP is obtained, for instance, from the resource constrained project scheduling problem (RCPSP) by choosing a resource and relaxing the constraints induced by the other resources. We state new properties on JPPS and we show that it can be used for studying the CuSP and for performing adjustments of heads and tails using a strategy very close to the one designed by Carlier and Pinson for the 1/ri, qi/Cmax sequencing problem. It confirms the interest of JPPS for solving RCPSP.