## Jackson’s pseudo-preemptive schedule and cumulative scheduling problems.(English)Zbl 1058.90023

Summary: 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 $$Pm/r_i, q_i/C_{\max}$$. 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) $$r_i$$, a processing time $$p_i$$, and a tail $$q_i$$. In the cumulative scheduling problem (CuSP), an operation $$i$$ requires a constant amount $$e_i$$ 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 $$1/r_i$$, $$q_i/C_{\max}$$ sequencing problem. It confirms the interest of JPPS for solving RCPSP.

### MSC:

 90B35 Deterministic scheduling theory in operations research