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In this paper, we are interested in parallel identical machine schedulingproblems with preemption and release dates in case of a regular criterion to beminimized. We show that solutions having a permutation flow shop structure aredominant if there exists an optimal solution with completion times scheduled inthe same order as the release dates, or if there is no release date. We alsoprove that, for a subclass of these problems, the completion times of all jobscan be ordered in an optimal solution. Using these two results, we provide newresults on polynomially solvable problems and hence refine the boundary betweenP and NP for these problems.

New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria