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Measuring the slack between lower bounds for scheduling on parallel machines

Author

Listed:
  • Jacques Carlier

    (UTC, Heudiasyc)

  • Claire Hanen

    (Sorbonne Université, CNRS, LIP6
    UPL, Université Paris Nanterre)

Abstract

This paper considers the problem of scheduling independent jobs with release dates and tails on m identical machines to minimize the makespan. The three main bounds are the preemptive bound, the energetic bound and the Jackson Pseudo Preemptive bound. It is known that they are very close in practice. The aim of this paper is to provide worst case instances where the slack between them is maximal and to prove tight bounds on the slack. We show that the slack is smaller than the maximal processing time.

Suggested Citation

  • Jacques Carlier & Claire Hanen, 2024. "Measuring the slack between lower bounds for scheduling on parallel machines," Annals of Operations Research, Springer, vol. 338(1), pages 347-377, July.
    • Handle: RePEc:spr:annopr:v:338:y:2024:i:1:d:10.1007_s10479-023-05759-8
    DOI: 10.1007/s10479-023-05759-8
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    References listed on IDEAS

    as
    1. Jacques Carlier & Abderrahim Sahli & Antoine Jouglet & Eric Pinson, 2022. "A faster checker of the energetic reasoning for the cumulative scheduling problem," International Journal of Production Research, Taylor & Francis Journals, vol. 60(11), pages 3419-3434, June.
    2. Carlier, Jacques, 1987. "Scheduling jobs with release dates and tails on identical machines to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 29(3), pages 298-306, June.
    3. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    4. Ph. Baptiste & C. Le Pape & W. Nuijten, 1999. "Satisfiability tests and time‐bound adjustmentsfor cumulative scheduling problems," Annals of Operations Research, Springer, vol. 92(0), pages 305-333, January.
    5. Hartmann, Sönke & Briskorn, Dirk, 2022. "An updated survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 1-14.
    6. J. Carlier & E. Pinson, 1998. "Jackson's Pseudo Preemptive Schedule for the Pm/r i , q i /C max scheduling problem," Annals of Operations Research, Springer, vol. 83(0), pages 41-58, October.
    Full references (including those not matched with items on IDEAS)

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