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Scheduling problems with two competing agents to minimize minmax and minsum earliness measures

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  • Mor, Baruch
  • Mosheiov, Gur

Abstract

A relatively new class of scheduling problems consists of multiple agents who compete on the use of a common processor. We focus in this paper on a two-agent setting. Each of the agents has a set of jobs to be processed on the same processor, and each of the agents wants to minimize a measure which depends on the completion times of its own jobs. The goal is to schedule the jobs such that the combined schedule performs well with respect to the measures of both agents. We consider measures of minmax and minsum earliness. Specifically, we focus on minimizing maximum earliness cost or total (weighted) earliness cost of one agent, subject to an upper bound on the maximum earliness cost of the other agent. We introduce a polynomial-time solution for the minmax problem, and prove NP-hardness for the weighted minsum case. The unweighted minsum problem is shown to have a polynomial-time solution.

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  • 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.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:3:p:540-546
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    Cited by:

    1. Baruch Mor & Gur Mosheiov, 2017. "A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1454-1468, May.
    2. Zhang, Xingong, 2021. "Two competitive agents to minimize the weighted total late work and the total completion time," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    3. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    4. 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.
    5. Shi-Sheng Li & Ren-Xia Chen & Qi Feng, 2016. "Scheduling two job families on a single machine with two competitive agents," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 784-799, October.
    6. Cheng, Shuenn-Ren, 2014. "Some new problems on two-agent scheduling to minimize the earliness costs," International Journal of Production Economics, Elsevier, vol. 156(C), pages 24-30.
    7. Shisheng Li & T.C.E. Cheng & C.T. Ng & Jinjiang Yuan, 2017. "Two‐agent scheduling on a single sequential and compatible batching machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 628-641, December.
    8. 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.
    9. Du-Juan Wang & Yunqiang Yin & Shuenn-Ren Cheng & T.C.E. Cheng & Chin-Chia Wu, 2016. "Due date assignment and scheduling on a single machine with two competing agents," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1152-1169, February.
    10. Lang, Fabian & Fink, Andreas & Brandt, Tobias, 2016. "Design of automated negotiation mechanisms for decentralized heterogeneous machine scheduling," European Journal of Operational Research, Elsevier, vol. 248(1), pages 192-203.
    11. Enrique Gerstl & Baruch Mor & Gur Mosheiov, 2017. "Scheduling with two competing agents to minimize total weighted earliness," Annals of Operations Research, Springer, vol. 253(1), pages 227-245, June.
    12. Mor, Baruch & Mosheiov, Gur, 2011. "Single machine batch scheduling with two competing agents to minimize total flowtime," European Journal of Operational Research, Elsevier, vol. 215(3), pages 524-531, December.
    13. Yunqiang Yin & Du‐Juan Wang & Chin‐Chia Wu & T.C.E. Cheng, 2016. "CON/SLK due date assignment and scheduling on a single machine with two agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(5), pages 416-429, August.
    14. Liang Tang & Zhihong Jin & Xuwei Qin & Ke Jing, 2019. "Supply chain scheduling in a collaborative manufacturing mode: model construction and algorithm design," Annals of Operations Research, Springer, vol. 275(2), pages 685-714, April.
    15. 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.
    16. 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.
    17. Koulamas, Christos, 2015. "A note on scheduling problems with competing agents and earliness minimization objectives," European Journal of Operational Research, Elsevier, vol. 245(3), pages 875-876.
    18. Perez-Gonzalez, Paz & Framinan, Jose M., 2014. "A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 1-16.
    19. Wang, Du-Juan & Yin, Yunqiang & Xu, Jianyou & Wu, Wen-Hsiang & Cheng, Shuenn-Ren & Wu, Chin-Chia, 2015. "Some due date determination scheduling problems with two agents on a single machine," International Journal of Production Economics, Elsevier, vol. 168(C), pages 81-90.
    20. 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.
    21. Enrique Gerstl & Gur Mosheiov, 2014. "Single machine just‐in‐time scheduling problems with two competing agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 1-16, February.
    22. Shang-Chia Liu & Jiahui Duan & Win-Chin Lin & Wen-Hsiang Wu & Jan-Yee Kung & Hau Chen & Chin-Chia Wu, 2018. "A Branch-and-Bound Algorithm for Two-Agent Scheduling with Learning Effect and Late Work Criterion," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.
    23. 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.
    24. 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.
    25. Yunqiang Yin & Youhua Chen & Kaida Qin & Dujuan Wang, 2019. "Two-agent scheduling on unrelated parallel machines with total completion time and weighted number of tardy jobs criteria," Journal of Scheduling, Springer, vol. 22(3), pages 315-333, June.

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