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Shared processor scheduling of multiprocessor jobs

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  • Dereniowski, Dariusz
  • Kubiak, Wiesław

Abstract

We study a problem of shared processor scheduling of multiprocessor weighted jobs. Each job can be executed on its private processor and simultaneously on possibly many processors shared by all jobs. This simultaneous execution reduces their completion times due to the processing time overlap. Each of the m shared processors may charge a different fee but otherwise the processors are identical. The goal is to maximize the total weighted overlap of all jobs. This is a key problem in subcontractor scheduling in extended enterprises and supply chains, and in divisible load scheduling in computing. We introduce synchronized schedules that complete each job that uses some shared processor at the same time on its private and on the shared processors. We prove that, quite surprisingly, the synchronized schedules include optimal ones. We obtain an α-approximation algorithm that runs in strongly polynomial time for the problem, where α=1/2+1/(4(m+1)). This improves the 1/2-approximation reported recently in the literature to 5/8-approximation for a single shared processor problem, m=1. The computational complexity of the problem, both in case of single and multi-shared processor, remains open. We show however an LP-based optimal algorithm for antithetical instances where for any pair of jobs j and i, if the processing time of j is smaller than or equal to the processing time of i, then the weight of j is greater than or equal to the weight of i.

Suggested Citation

  • Dereniowski, Dariusz & Kubiak, Wiesław, 2020. "Shared processor scheduling of multiprocessor jobs," European Journal of Operational Research, Elsevier, vol. 282(2), pages 464-477.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:2:p:464-477
    DOI: 10.1016/j.ejor.2019.09.033
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    References listed on IDEAS

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    1. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
    2. Dariusz Dereniowski & Wiesław Kubiak, 2018. "Shared processor scheduling," Journal of Scheduling, Springer, vol. 21(6), pages 583-593, December.
    3. George L. Vairaktarakis, 2013. "Noncooperative Games for Subcontracting Operations," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 148-158, September.
    4. Dereniowski, Dariusz & Kubiak, Wiesław, 2017. "Shared multi-processor scheduling," European Journal of Operational Research, Elsevier, vol. 261(2), pages 503-514.
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