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Two-agent scheduling of unit processing time jobs to minimize total weighted completion time and total weighted number of tardy jobs

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  • Wan, Long
  • Mei, Jiajie
  • Du, Jiangze

Abstract

In this paper, we revisit a two-agent scheduling problem on a single machine with jobs of unit processing times. In this problem, we have two agents: agent A and agent B. Each agent has his/her own disjoint job set. The objective of agent A is to minimize the total weighted completion time, and the objective of agent B is to minimize the total weighted number of tardy jobs. The complexity of the decision version of the problem was proposed as open in Oron et al. (European Journal of Operational Research 244:86–99, 2015). We construct a reduction from a variant of Even-Odd Partition to show that this problem is NP-complete. Finally, we also propose a pseudo-polynomial algorithm and a dual FPTAS for the problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:290:y:2021:i:1:p:26-35
    DOI: 10.1016/j.ejor.2020.07.064
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    References listed on IDEAS

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    4. Gao, Yuan & Yuan, Jinjiang & Ng, C.T. & Cheng, T.C.E., 2019. "A further study on two-agent parallel-batch scheduling with release dates and deteriorating jobs to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 273(1), pages 74-81.
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    13. Tang, Lixin & Zhao, Xiaoli & Liu, Jiyin & Leung, Joseph Y.-T., 2017. "Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine," European Journal of Operational Research, Elsevier, vol. 263(2), pages 401-411.
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    Cited by:

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    2. Li-Han Zhang & Dan-Yang Lv & Ji-Bo Wang, 2023. "Two-Agent Slack Due-Date Assignment Scheduling with Resource Allocations and Deteriorating Jobs," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    3. Wang, Julong & Liu, Zhixue & Li, Feng, 2024. "Integrated production and transportation scheduling problem under nonlinear cost structures," European Journal of Operational Research, Elsevier, vol. 313(3), pages 883-904.
    4. Chen, Ke & Cheng, T.C.E. & Huang, Hailiang & Ji, Min & Yao, Danli, 2023. "Single-machine scheduling with autonomous and induced learning to minimize total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 24-34.
    5. 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.

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