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Pareto-optimal Algorithms for Scheduling Games on Parallel-batching Machines with Activation Cost

Author

Listed:
  • Long Zhang

    (School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Ji’nan, Shandong 250014, P. R. China2School of Management, Qufu Normal University, Rizhao, Shandong 276826, P. R. China)

  • Jiguo Yu

    (School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Ji’nan, Shandong 250014, P. R. China)

  • Yuzhong Zhang

    (Institute of Operations Research, Qufu Normal University, Rizhao, Shandong 276826, P. R. China)

Abstract

We study one scheduling game with activation cost, where each game involves n jobs being processed on m parallel-batching identical machines. Each job, as an agent, selects a machine (more precisely, a batch on a machine) for processing to minimize his disutility, which consists of the load of his machine and his share in the machine’s activation cost. We prove that Nash equilibrium may not exist for the scheduling game. We design a polynomial-time algorithm to produce pareto-optimal schedules for two special cases of the scheduling game. Finally, we show that the general form of the scheduling game has pareto-optimal schedule by an improved polynomial-time algorithm, and prove that the schedule is a tight 𝜖-approximate Nash equilibria.

Suggested Citation

  • Long Zhang & Jiguo Yu & Yuzhong Zhang, 2021. "Pareto-optimal Algorithms for Scheduling Games on Parallel-batching Machines with Activation Cost," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(05), pages 1-15, October.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400078
    DOI: 10.1142/S0217595921400078
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