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Algorithms for single machine scheduling problem with release dates and submodular penalties

Author

Listed:
  • Xiaofei Liu

    (Yunnan University)

  • Man Xiao

    (Yunnan University)

  • Weidong Li

    (Yunnan University)

  • Yaoyu Zhu

    (Peking University)

  • Lei Ma

    (Beijing Academy of Artificial Intelligence
    Peking University)

Abstract

In this paper, we consider the single machine scheduling problem with release dates and submodular penalties, in which each job can be either assigned to the machine or rejected. The objective is to minimize the sum of the makespan of the processed jobs and the penalty of the rejected jobs which is determined by a submodular function. First, we present a simple algorithm for the off-line problem. Second, for the on-line problem, we prove that there is no on-line algorithm with a constant competitive ratio if the penalty submodular function is not monotone, and present an on-line algorithm with a competitive ratio of 3 if the penalty submodular function is monotone. Finally, we consider a special case of the on-line problem in which all jobs have the same release date. We prove that there is no on-line algorithm with a competitive ratio of $$\frac{\sqrt{5}+1}{2}\approx 1.618$$ 5 + 1 2 ≈ 1.618 , and the competitive ratio of the on-line algorithm we presented is 2.

Suggested Citation

  • Xiaofei Liu & Man Xiao & Weidong Li & Yaoyu Zhu & Lei Ma, 2023. "Algorithms for single machine scheduling problem with release dates and submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-18, May.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:4:d:10.1007_s10878-023-01032-7
    DOI: 10.1007/s10878-023-01032-7
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    References listed on IDEAS

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    1. Hongye Zheng & Suogang Gao & Wen Liu & Weili Wu & Ding-Zhu Du & Bo Hou, 2022. "Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 343-353, August.
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    11. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    12. Xiaofei Liu & Weidong Li, 2020. "Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    13. Xueling Zhong & Zhangming Pan & Dakui Jiang, 2017. "Scheduling with release times and rejection on two parallel machines," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 934-944, April.
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