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Shortest path to nonpreemptive schedules of unit-time jobs on two identical parallel machines with minimum total completion time

Author

Listed:
  • Philippe Baptiste
  • Vadim G. Timkovsky

Abstract

Ideal schedules reach both minimum maximum completion time and minimum total completion time of jobs. It is known that there exist computable in polynomial time ideal nonpreemptive two-machine schedules of unit-time operation jobs with equal release dates and arbitrary precedence constraints on identical parallel machines, in flow shops and open shops. In this paper, we study the possibility of extending these results to the case where release dates can be different. We establish the complexity status of P2|prec,r j ,p j =1|∑C j and F2|prec,r j ,p ij =1|∑C j showing that optimal schedules for these problems can also be found in polynomial time and conjecture that all such schedules are ideal indeed. On the other hand, we show that the ideal schedules in open shops do not always exist. Copyright Springer-Verlag 2004

Suggested Citation

  • Philippe Baptiste & Vadim G. Timkovsky, 2004. "Shortest path to nonpreemptive schedules of unit-time jobs on two identical parallel machines with minimum total completion time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(1), pages 145-153, September.
    • Handle: RePEc:spr:mathme:v:60:y:2004:i:1:p:145-153
    DOI: 10.1007/s001860300336
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    Citations

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    Cited by:

    1. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2021. "Ideal schedules in parallel machine settings," European Journal of Operational Research, Elsevier, vol. 290(2), pages 422-434.
    2. Bo Chen & Ed Coffman & Dariusz Dereniowski & Wiesław Kubiak, 2016. "Normal-form preemption sequences for an open problem in scheduling theory," Journal of Scheduling, Springer, vol. 19(6), pages 701-728, December.
    3. D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.

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