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Scheduling with periodic availability constraints to minimize makespan

Author

Listed:
  • Lishi Yu

    (Zhejiang University)

  • Zhiyi Tan

    (Zhejiang University)

Abstract

We study scheduling problems with periodic availability constraints. Each machine is periodically unavailable due to routine arrangements or regular maintenance. The availability periods and unavailability periods, each with the same duration, appear alternately on each machine. All jobs are available at time zero, and no job preemption is allowed. The objective is to minimize the makespan. We conduct the worst-case analysis of two algorithms, SFFD and DFFD, with respect to parameter $$\beta $$ β , the ratio between the length of an unavailability period and an availability period. For the single machine problem, the worst-case ratio of the algorithm SFFD is given, and the bound is tight when $$\beta >0.1022$$ β > 0.1022 . An algorithm with a worst-case ratio arbitrarily close to $$\frac{2\beta +2}{\beta +2}$$ 2 β + 2 β + 2 is also presented. For the two machines problem, we propose a new algorithm DFFD and show its tight worst-case ratio.

Suggested Citation

  • Lishi Yu & Zhiyi Tan, 2024. "Scheduling with periodic availability constraints to minimize makespan," Journal of Scheduling, Springer, vol. 27(3), pages 277-297, June.
    • Handle: RePEc:spr:jsched:v:27:y:2024:i:3:d:10.1007_s10951-023-00790-w
    DOI: 10.1007/s10951-023-00790-w
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