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An algorithm for multi-agent scheduling to minimize the makespan on m parallel machines

Author

Listed:
  • Manzhan Gu

    (School of Mathematics, Shanghai University of Finance and Economics)

  • Jinwei Gu

    (Shanghai University of Electric Power)

  • Xiwen Lu

    (East China University of Science and Technology)

Abstract

This paper considers a multi-agent scheduling problem, in which each agent has a set of non-preemptive jobs, and jobs of all agents are to be processed on m identical parallel machines. The objective is to find a schedule to minimize the makespan of each agent. For an agent, the definition of $$\alpha $$ α point is introduced, based on which an approximation algorithm is proposed for the problem. In the obtained schedule, the agent with the ith smallest $$\alpha $$ α point value is the ith completed agent, and the agent’s completion time is at most $$i+ \left( \frac{1}{3}-\frac{1}{3m}\right) $$ i + 1 3 - 1 3 m times its minimum makespan. Finally, we show the performance analysis is tight.

Suggested Citation

  • Manzhan Gu & Jinwei Gu & Xiwen Lu, 2018. "An algorithm for multi-agent scheduling to minimize the makespan on m parallel machines," Journal of Scheduling, Springer, vol. 21(5), pages 483-492, October.
    • Handle: RePEc:spr:jsched:v:21:y:2018:i:5:d:10.1007_s10951-017-0546-9
    DOI: 10.1007/s10951-017-0546-9
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    References listed on IDEAS

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    1. 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.
    2. Kejun Zhao & Xiwen Lu & Manzhan Gu, 2016. "A new approximation algorithm for multi-agent scheduling to minimize makespan on two machines," Journal of Scheduling, Springer, vol. 19(1), pages 21-31, February.
    3. 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.
    4. Alessandro Agnetis & Dario Pacciarelli & Andrea Pacifici, 2007. "Multi-agent single machine scheduling," Annals of Operations Research, Springer, vol. 150(1), pages 3-15, March.
    5. Kejun Zhao & Xiwen Lu, 2016. "Two approximation algorithms for two-agent scheduling on parallel machines to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 260-278, January.
    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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    Cited by:

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    2. Jun Pei & Jinling Wei & Baoyu Liao & Xinbao Liu & Panos M. Pardalos, 2020. "Two-agent scheduling on bounded parallel-batching machines with an aging effect of job-position-dependent," Annals of Operations Research, Springer, vol. 294(1), pages 191-223, November.
    3. 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.
    4. Jesús Isaac Vázquez-Serrano & Leopoldo Eduardo Cárdenas-Barrón & Rodrigo E. Peimbert-García, 2021. "Agent Scheduling in Unrelated Parallel Machines with Sequence- and Agent–Machine–Dependent Setup Time Problem," Mathematics, MDPI, vol. 9(22), pages 1-34, November.

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