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Pareto optimization scheduling with two competing agents to minimize the number of tardy jobs and the maximum cost

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  • Wan, Long
  • Yuan, Jinjiang
  • Wei, Lijun

Abstract

This paper investigates the Pareto optimization scheduling problem on a single machine with two competing agents A and B in which agent A wants to minimize the number of tardy A-jobs and agent B wants to minimize the maximum cost of B-jobs. In the literature, the constrained optimization problem of minimizing the number of tardy A-jobs under the restriction that the maximum cost of B-jobs is bounded is solved in polynomial time. This implies that the corresponding Pareto optimization scheduling problem can be solved in a weakly polynomial time. In this paper, by presenting a new algorithm for the constrained optimization problem, we provide a strongly polynomial-time algorithm for the corresponding Pareto optimization scheduling problem. Experimentation results show that the proposed algorithm for the considered problem is efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:912-923
    DOI: 10.1016/j.amc.2015.10.059
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    References listed on IDEAS

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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.
    2. 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.
    3. Xiaoling Cao & Wen-Hsing Wu & Wen-Hung Wu & Chin-Chia Wu, 2018. "Some two-agent single-machine scheduling problems to minimize minmax and minsum of completion times," Operational Research, Springer, vol. 18(2), pages 293-314, July.
    4. Yuan Zhang & Jinjiang Yuan & Chi To Ng & Tai Chiu E. Cheng, 2021. "Pareto‐optimization of three‐agent scheduling to minimize the total weighted completion time, weighted number of tardy jobs, and total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 378-393, April.
    5. Wan, Long & Mei, Jiajie & Du, Jiangze, 2021. "Two-agent scheduling of unit processing time jobs to minimize total weighted completion time and total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 290(1), pages 26-35.
    6. Shi-Sheng Li & Ren-Xia Chen, 2023. "Competitive two-agent scheduling with release dates and preemption on a single machine," Journal of Scheduling, Springer, vol. 26(3), pages 227-249, June.
    7. Ruyan He & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2021. "Two-agent preemptive Pareto-scheduling to minimize the number of tardy jobs and total late work," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 504-525, February.

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