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Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties

Author

Listed:
  • Hongye Zheng

    (Hebei Normal University)

  • Suogang Gao

    (Hebei Normal University)

  • Wen Liu

    (Hebei Normal University)

  • Weili Wu

    (University of Texas at Dallas)

  • Ding-Zhu Du

    (University of Texas at Dallas)

  • Bo Hou

    (Hebei Normal University)

Abstract

In this paper, we consider the parallel-machine scheduling problem with release dates and submodular rejection penalties. In this problem, we are given m identical parallel machines and n jobs. Each job has a processing time and a release date. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on one of the m identical parallel machines. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a submodular function. Our main work is to design a 2-approximation algorithm based on the primal-dual framework.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00842-x
    DOI: 10.1007/s10878-021-00842-x
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    References listed on IDEAS

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    1. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
    2. Xianzhao Zhang & Dachuan Xu & Donglei Du & Chenchen Wu, 2018. "Approximation algorithms for precedence-constrained identical machine scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 318-330, January.
    3. Yuri N. Sotskov & Natalja G. Egorova, 2019. "The Optimality Region for a Single-Machine Scheduling Problem with Bounded Durations of the Jobs and the Total Completion Time Objective," Mathematics, MDPI, vol. 7(5), pages 1-21, April.
    4. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.
    5. 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.
    6. 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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    Cited by:

    1. 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.

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