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Two-agent scheduling in a two-machine open shop

Author

Listed:
  • Peihai Liu

    (East China University of Science and Technology)

  • Manzhan Gu

    (Shanghai University of Finance and Economics)

  • Xiwen Lu

    (East China University of Science and Technology)

Abstract

This paper considers several two-machine open shop problems with two agents. Each agent has an independent set of nonpreemptive jobs, and the objective is to find either a schedule minimizing a linear combination of the makespans of both agents, a schedule minimizing the makespan of one agent with the makespan of the other agent not exceeding a threshold, or all Pareto-optimal schedules with respect to the makespans of both agents. We present a number of results for the problems above, including a polynomial algorithm and a pseudo-polynomial algorithm for special cases, non-approximability, two approximation algorithms, and a fully polynomial-time approximation scheme. Finally, we run numerical experiments to show the effectiveness of the pseudo-polynomial algorithm and the approximation algorithms.

Suggested Citation

  • Peihai Liu & Manzhan Gu & Xiwen Lu, 2024. "Two-agent scheduling in a two-machine open shop," Annals of Operations Research, Springer, vol. 333(1), pages 275-301, February.
    • Handle: RePEc:spr:annopr:v:333:y:2024:i:1:d:10.1007_s10479-023-05780-x
    DOI: 10.1007/s10479-023-05780-x
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    References listed on IDEAS

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    1. Wenchang Luo & Lin Chen & Guochuan Zhang, 2012. "Approximation schemes for two-machine flow shop scheduling with two agents," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 229-239, October.
    2. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    3. Mor, Baruch & Mosheiov, Gur, 2010. "Scheduling problems with two competing agents to minimize minmax and minsum earliness measures," European Journal of Operational Research, Elsevier, vol. 206(3), pages 540-546, November.
    4. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    5. Byung-Gyoo Kim & Byung-Cheon Choi & Myoung-Ju Park, 2017. "Two-Machine and Two-Agent Flow Shop with Special Processing Times Structures," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-17, August.
    6. Byung-Cheon Choi & Myoung-Ju Park, 2016. "An Ordered Flow Shop with Two Agents," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-24, October.
    7. Nong, Q.Q. & Cheng, T.C.E. & Ng, C.T., 2011. "Two-agent scheduling to minimize the total cost," European Journal of Operational Research, Elsevier, vol. 215(1), pages 39-44, November.
    8. B Mor & G Mosheiov, 2014. "Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(1), pages 151-157, January.
    9. Donatas Elvikis & Vincent T’kindt, 2014. "Two-agent scheduling on uniform parallel machines with min-max criteria," Annals of Operations Research, Springer, vol. 213(1), pages 79-94, February.
    10. Cheng He & Chunqi Xu & Hao Lin, 2020. "Serial-batching scheduling with two agents to minimize makespan and maximum cost," Journal of Scheduling, Springer, vol. 23(5), pages 609-617, October.
    11. A. Agnetis & P.B. Mirchandani & D. Pacciarelli & A. Pacifici, 2000. "Nondominated Schedules for a Job-Shop with Two Competing Users," Computational and Mathematical Organization Theory, Springer, vol. 6(2), pages 191-217, July.
    12. Fan, B.Q. & Cheng, T.C.E., 2016. "Two-agent scheduling in a flowshop," European Journal of Operational Research, Elsevier, vol. 252(2), pages 376-384.
    13. Joseph Y.-T. Leung & Michael Pinedo & Guohua Wan, 2010. "Competitive Two-Agent Scheduling and Its Applications," Operations Research, INFORMS, vol. 58(2), pages 458-469, April.
    14. 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.
    15. Yuan Gao & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2022. "Pareto-scheduling with family jobs or ND-agent on a parallel-batch machine to minimize the makespan and maximum cost," 4OR, Springer, vol. 20(2), pages 273-287, June.
    16. Balasubramanian, Hari & Fowler, John & Keha, Ahmet & Pfund, Michele, 2009. "Scheduling interfering job sets on parallel machines," European Journal of Operational Research, Elsevier, vol. 199(1), pages 55-67, November.
    17. Choi, Byung-Cheon & Park, Myoung-Ju, 2017. "Two-agent parallel machine scheduling with a restricted number of overlapped reserved tasks," European Journal of Operational Research, Elsevier, vol. 260(2), pages 514-519.
    18. 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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