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A coordination mechanism for a scheduling game with parallel-batching machines

Author

Listed:
  • Q. Q. Nong

    (Ocean University of China)

  • G. Q. Fan

    (Ocean University of China)

  • Q. Z. Fang

    (Ocean University of China)

Abstract

In this paper we consider the scheduling problem with parallel-batching machines from a game theoretic perspective. There are m parallel-batching machines each of which can handle up to b jobs simultaneously as a batch. The processing time of a batch is the time required for processing the longest job in the batch, and all the jobs in a batch start and complete at the same time. There are n jobs. Each job is owned by a rational and selfish agent and its individual cost is the completion time of its job. The social cost is the largest completion time over all jobs, the makespan. We design a coordination mechanism for the scheduling game problem. We discuss the existence of pure Nash Equilibria and offer upper and lower bounds on the price of anarchy of the coordination mechanism. We show that the mechanism has a price of anarchy no more than $$2-\frac{2}{3b}-\frac{1}{3\max \{m,b\}}$$ 2 - 2 3 b - 1 3 max { m , b } .

Suggested Citation

  • Q. Q. Nong & G. Q. Fan & Q. Z. Fang, 2017. "A coordination mechanism for a scheduling game with parallel-batching machines," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 567-579, February.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-015-9980-9
    DOI: 10.1007/s10878-015-9980-9
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    References listed on IDEAS

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    1. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
    2. Schuurman, P. & Vredeveld, T., 2005. "Performance guarantees of local search for multiprocessor scheduling," Research Memorandum 055, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    4. Petra Schuurman & Tjark Vredeveld, 2007. "Performance Guarantees of Local Search for Multiprocessor Scheduling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 52-63, February.
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    Cited by:

    1. Jun-Qiang Wang & Guo-Qiang Fan & Zhixin Liu, 2020. "Mixed batch scheduling on identical machines," Journal of Scheduling, Springer, vol. 23(4), pages 487-496, August.
    2. Cong Chen & Yinfeng Xu, 0. "Coordination mechanisms for scheduling selfish jobs with favorite machines," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-33.
    3. Cong Chen & Yinfeng Xu, 2020. "Coordination mechanisms for scheduling selfish jobs with favorite machines," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 333-365, August.

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