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Parametric analysis of the quality of single preemption schedules on three uniform parallel machines

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  • Alan J. Soper

    (University of Greenwich)

  • Vitaly A. Strusevich

    (University of Greenwich)

Abstract

For a scheduling problem to minimize the makespan on three uniform parallel machines we present a parametric analysis of the quality of a schedule with at most one preemption compared to the global optimal schedule with any number of preemptions. A tight bound is derived as a function of the relative speeds of the machines, provided that two of the machines have the same speed.

Suggested Citation

  • Alan J. Soper & Vitaly A. Strusevich, 2021. "Parametric analysis of the quality of single preemption schedules on three uniform parallel machines," Annals of Operations Research, Springer, vol. 298(1), pages 469-495, March.
    • Handle: RePEc:spr:annopr:v:298:y:2021:i:1:d:10.1007_s10479-018-2952-6
    DOI: 10.1007/s10479-018-2952-6
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    References listed on IDEAS

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    1. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    2. Kabir Rustogi & Vitaly A. Strusevich, 2013. "Parallel Machine Scheduling: Impact of Adding Extra Machines," Operations Research, INFORMS, vol. 61(5), pages 1243-1257, October.
    3. Evgeny Shchepin & Nodari Vakhania, 2008. "On the geometry, preemptions and complexity of multiprocessor and shop scheduling," Annals of Operations Research, Springer, vol. 159(1), pages 183-213, March.
    4. Yiwei Jiang & Zewei Weng & Jueliang Hu, 2014. "Algorithms with limited number of preemptions for scheduling on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 711-723, May.
    5. José R. Correa & Martin Skutella & José Verschae, 2012. "The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 379-398, May.
    6. Paul Mireault & James B. Orlin & Rakesh V. Vohra, 1997. "A Parametric Worst Case Analysis of the LPT Heuristic for Two Uniform Machines," Operations Research, INFORMS, vol. 45(1), pages 116-125, February.
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    Cited by:

    1. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    2. Alan J. Soper & Vitaly A. Strusevich, 2022. "Preemptive and non-preemptive scheduling on two unrelated parallel machines," Journal of Scheduling, Springer, vol. 25(6), pages 659-674, December.

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