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An online joint replenishment problem combined with single machine scheduling

Author

Listed:
  • Péter Györgyi

    (ELKH Institute for Computer Science and Control)

  • Tamás Kis

    (ELKH Institute for Computer Science and Control)

  • Tímea Tamási

    (ELKH Institute for Computer Science and Control
    ELTE Eötvös Loránd University)

Abstract

This paper considers a combination of the joint replenishment problem with single machine scheduling. There is a single resource, which is required by all the unit-time jobs, and a job can be started at time point t on the machine if and only if the machine does not process another job at t, and the resource is replenished between its release date and t. Each replenishment has a cost, which is independent of the amount replenished. The objective is to minimize the total replenishment cost plus the maximum flow time of the jobs. We consider the online variant of the problem, where the jobs are released over time, and once a job is inserted into the schedule, its starting time cannot be changed. We propose a deterministic 2-competitive online algorithm for the general input. Moreover, we show that for a certain class of inputs (so-called p-bounded input), the competitive ratio of the algorithm tends to $$\sqrt{2}$$ 2 as the number of jobs tends to infinity. We also derive several lower bounds for the best competitive ratio of any deterministic online algorithm under various assumptions.

Suggested Citation

  • Péter Györgyi & Tamás Kis & Tímea Tamási, 2023. "An online joint replenishment problem combined with single machine scheduling," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-20, July.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:5:d:10.1007_s10878-023-01064-z
    DOI: 10.1007/s10878-023-01064-z
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    References listed on IDEAS

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    1. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    2. Péter Györgyi & Tamás Kis & Tímea Tamási & József Békési, 2023. "Joint replenishment meets scheduling," Journal of Scheduling, Springer, vol. 26(1), pages 77-94, February.
    3. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2006. "Primal-Dual Algorithms for Deterministic Inventory Problems," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 267-284, May.
    4. Niv Buchbinder & Tracy Kimbrel & Retsef Levi & Konstantin Makarychev & Maxim Sviridenko, 2013. "Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms," Operations Research, INFORMS, vol. 61(4), pages 1014-1029, August.
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