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Single machine scheduling with two competing agents, arbitrary release dates and unit processing times

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  • Omri Dover

    (Ben-Gurion University of the Negev)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

Abstract

We study various single machine scheduling problems with two competing agents, unit processing times and arbitrary integer release dates. The problems differ by the scheduling criterion used by each of the two agents, and by the variant of the bicriteria problem that has to be solved. We prove that when the scheduling criterion of either one of the two agents is of a max-type, then all considered variants of the bicriteria problem are solvable in polynomial time. However, when the two agents have a sum-type of scheduling criterion, several variants of the bicriteria problem become $$\mathcal {NP}$$ NP -hard.

Suggested Citation

  • Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2054-7
    DOI: 10.1007/s10479-015-2054-7
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    References listed on IDEAS

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    Cited by:

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    2. Zhang, Haowei & Xie, Junwei & Ge, Jiaang & Zhang, Zhaojian & Zong, Binfeng, 2019. "A hybrid adaptively genetic algorithm for task scheduling problem in the phased array radar," European Journal of Operational Research, Elsevier, vol. 272(3), pages 868-878.
    3. Shesh Narayan Sahu & Yuvraj Gajpal & Swapan Debbarma, 2018. "Two-agent-based single-machine scheduling with switchover time to minimize total weighted completion time and makespan objectives," Annals of Operations Research, Springer, vol. 269(1), pages 623-640, October.
    4. Yunqiang Yin & Doudou Li & Dujuan Wang & T. C. E. Cheng, 2021. "Single-machine serial-batch delivery scheduling with two competing agents and due date assignment," Annals of Operations Research, Springer, vol. 298(1), pages 497-523, March.
    5. 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.
    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.

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