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Two-agent scheduling to minimize the total cost

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  • Nong, Q.Q.
  • Cheng, T.C.E.
  • Ng, C.T.

Abstract

Two agents, each having his own set of jobs, compete to perform their own jobs on a common processing resource. Each job of the agents has a weight that specifies its importance. The cost of the first agent is the maximum weighted completion time of his jobs while the cost of the second agent is the total weighted completion time of his jobs. We consider the scheduling problem of determining the sequence of the jobs such that the total cost of the two agents is minimized. We provide a 2-approximation algorithm for the problem, show that the case where the number of jobs of the first agent is fixed is NP-hard, and devise a polynomial time approximation scheme for this case.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:1:p:39-44
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    References listed on IDEAS

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    6. Cheng, T.C.E. & Ng, C.T. & Yuan, J.J., 2008. "Multi-agent scheduling on a single machine with max-form criteria," European Journal of Operational Research, Elsevier, vol. 188(2), pages 603-609, July.
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    Citations

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    Cited by:

    1. Wan, Long & Ding, Zhihao & Li, Yunpeng & Chen, Qianqian & Tan, Zhiyi, 2015. "Scheduling to minimize the maximum total completion time per machine," European Journal of Operational Research, Elsevier, vol. 242(1), pages 45-50.
    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. Yaodong Ni & Zhaojun Zhao, 2017. "Two-agent scheduling problem under fuzzy environment," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 739-748, March.
    4. 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.
    5. Xing Chai & Lingfa Lu & Wenhua Li & Liqi Zhang, 2018. "Best-Possible Online Algorithms for Single Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-11, December.
    6. 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.
    7. 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.
    8. 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.
    9. Castillo, Berenice & Grogan-Kaylor, Andrew & Gleeson, Shannon M. & Ma, Julie, 2020. "Child externalizing behavior in context: Associations of mother nonstandard work, parenting, and neighborhoods," Children and Youth Services Review, Elsevier, vol. 116(C).

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