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W-prize-collecting scheduling problem on parallel machines

Author

Listed:
  • Bo Hou

    (Hebei Normal University)

  • Tianjiao Guo

    (Hebei Normal University)

  • Suogang Gao

    (Hebei Normal University)

  • Guanghua Wang

    (University of Texas at Dallas)

  • Weili Wu

    (University of Texas at Dallas)

  • Wen Liu

    (Hebei Normal University)

Abstract

In this paper, we consider the W-prize-collecting scheduling problem on parallel machines. In this problem, we are given a set of n jobs, a set of m identical parallel machines and a value W. Each job $$J_j$$ J j has a processing time, a profit and a rejection penalty. Each job is either accepted and processed on one of the machines without preemption, or rejected and paid a rejection penalty. The objective is to minimize the sum of the makespan of accepted jobs and the penalties of rejected jobs, and at the same time the total profit brought by accepted jobs is not less than W. We design a 2-approximation algorithm for the problem based on the greedy method and the list scheduling algorithm.

Suggested Citation

  • Bo Hou & Tianjiao Guo & Suogang Gao & Guanghua Wang & Weili Wu & Wen Liu, 2024. "W-prize-collecting scheduling problem on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-9, October.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:3:d:10.1007_s10878-024-01212-z
    DOI: 10.1007/s10878-024-01212-z
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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.
    2. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.
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