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A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Author

Listed:
  • Wencheng Wang

    (School of Mathematics and Statistics, Yunnan University, Kunming 650500, China
    These authors contributed equally to this work.)

  • Xiaofei Liu

    (School of Information Science and Engineering, Yunnan University, Kunming 650500, China
    School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, China
    These authors contributed equally to this work.)

Abstract

In this paper, we consider parallel-machine scheduling with release times and submodular penalties ( P | r j , r e j e c t | C max + π ( R ) ), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P | r j , r e j e c t | C max + π ( R ) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P | r j , r e j e c t | C max + π ( R ) . This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

Suggested Citation

  • Wencheng Wang & Xiaofei Liu, 2021. "A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties," Mathematics, MDPI, vol. 10(1), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:61-:d:711094
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    References listed on IDEAS

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    1. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.
    2. Ou, Jinwen & Zhong, Xueling & Wang, Guoqing, 2015. "An improved heuristic for parallel machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 241(3), pages 653-661.
    3. 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.
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