The aim of this paper is to introduce Jackson's Pseudo Preemptive Schedule (JPPS) for the m parallel and identical processor scheduling problem Pm/ri, qi /Cmax. JPPS generalizes Jackson's Preemptive Schedule (JPS) which was introduced for the one-processor sequencing problem 1/ri, qi /Cmax. JPS can be computed in O(n log n) time and plays a central role in solving NP-hard disjunctive scheduling problems such as the job shop problem. The makespan of JPPS can be computed in O(n log n + nm log m) time, and is a tight lower bound for the Pm/Ri, qi /Cmax problem. So JPPS could also play a central role in solving the Resource Constrained Project Scheduling Problem.
