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Two-Agent Pareto-Scheduling of Minimizing Total Weighted Completion Time and Total Weighted Late Work

Author

Listed:
  • Yuan Zhang

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
    These authors contributed equally to this work.)

  • Zhichao Geng

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
    These authors contributed equally to this work.)

  • Jinjiang Yuan

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
    These authors contributed equally to this work.)

Abstract

We investigate the Pareto-scheduling problem with two competing agents on a single machine to minimize the total weighted completion time of agent A ’s jobs and the total weighted late work of agent B ’s jobs, the B -jobs having a common due date. Since this problem is known to be NP-hard, we present two pseudo-polynomial-time exact algorithms to generate the Pareto frontier and an approximation algorithm to generate a ( 1 + ϵ ) -approximate Pareto frontier. In addition, some numerical tests are undertaken to evaluate the effectiveness of our algorithms.

Suggested Citation

  • Yuan Zhang & Zhichao Geng & Jinjiang Yuan, 2020. "Two-Agent Pareto-Scheduling of Minimizing Total Weighted Completion Time and Total Weighted Late Work," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2070-:d:448030
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    References listed on IDEAS

    as
    1. Yunqiang Yin & T. C. E. Cheng & Du-Juan Wang & Chin-Chia Wu, 2017. "Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs," Journal of Scheduling, Springer, vol. 20(4), pages 313-335, August.
    2. Yuan Zhang & Jinjiang Yuan, 2019. "A note on a two-agent scheduling problem related to the total weighted late work," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 989-999, April.
    3. Wan, Long & Yuan, Jinjiang & Wei, Lijun, 2016. "Pareto optimization scheduling with two competing agents to minimize the number of tardy jobs and the maximum cost," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 912-923.
    4. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    5. Yin, Yunqiang & Cheng, Shuenn-Ren & Cheng, T.C.E. & Wang, Du-Juan & Wu, Chin-Chia, 2016. "Just-in-time scheduling with two competing agents on unrelated parallel machines," Omega, Elsevier, vol. 63(C), pages 41-47.
    6. Cheng He & Joseph Y.-T. Leung, 2017. "Two-agent scheduling of time-dependent jobs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 362-377, August.
    7. A. M. A. Hariri & C. N. Potts & L. N. Van Wassenhove, 1995. "Single Machine Scheduling to Minimize Total Weighted Late Work," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 232-242, May.
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    Cited by:

    1. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.

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