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Choosing a batch to be processed

Author

Listed:
  • Tzvi Alon

    (The Hebrew University of Jerusalem)

  • Moshe Haviv

    (The Hebrew University of Jerusalem
    The Chinese University of Hong Kong)

Abstract

Suppose identical jobs need to be processed by a single processor. Processing is carried out one job after the other, in batches, and jobs are released only when their entire batch is done. Each job is held by an agent, who tries to minimize costs. The cost of an individual job is linear in two terms: a congestion cost, dependent on the size of the batch, and a lateness cost, dependent also on the number of jobs preceding the batch. The agents need to decide on the sequential index of the batch they ascribe to. This decision problem is stated as a non-cooperative game, with applications both in ride sharing and in queues in which the server must never be idle. We derive its (mixed) symmetric equilibrium, which always exists, and its pure non-symmetric equilibrium, when it exists. The corresponding social optimization problem is solved as well, leading, in the mixed symmetric case, to an explicit formula for the price of anarchy.

Suggested Citation

  • Tzvi Alon & Moshe Haviv, 2023. "Choosing a batch to be processed," Annals of Operations Research, Springer, vol. 326(1), pages 67-87, July.
    • Handle: RePEc:spr:annopr:v:326:y:2023:i:1:d:10.1007_s10479-023-05274-w
    DOI: 10.1007/s10479-023-05274-w
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    References listed on IDEAS

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    1. Amihai Glazer & Refael Hassin & Liron Ravner, 2018. "A strategic model of job arrivals to a single machine with earliness and tardiness penalties," IISE Transactions, Taylor & Francis Journals, vol. 50(4), pages 265-278, April.
    2. Colin E. Bell & Shaler Stidham, Jr., 1983. "Individual versus Social Optimization in the Allocation of Customers to Alternative Servers," Management Science, INFORMS, vol. 29(7), pages 831-839, July.
    3. Harsha Honnappa & Rahul Jain, 2015. "Strategic Arrivals into Queueing Networks: The Network Concert Queueing Game," Operations Research, INFORMS, vol. 63(1), pages 247-259, February.
    4. Rapoport, Amnon & Stein, William E. & Parco, James E. & Seale, Darryl A., 2004. "Equilibrium play in single-server queues with endogenously determined arrival times," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 67-91, September.
    5. Refael Hassin & Yana Kleiner, 2011. "Equilibrium and optimal arrival patterns to a server with opening and closing times," IISE Transactions, Taylor & Francis Journals, vol. 43(3), pages 164-175.
    6. Jesper Breinbjerg & Alexander Sebald & Lars Peter Østerdal, 2016. "Strategic behavior and social outcomes in a bottleneck queue: experimental evidence," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 207-236, September.
    7. Glazer, Amihai & Hassin, Refael, 1983. "?/M/1: On the equilibrium distribution of customer arrivals," European Journal of Operational Research, Elsevier, vol. 13(2), pages 146-150, June.
    8. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.
    9. Moshe Haviv & Liron Ravner, 2021. "A survey of queueing systems with strategic timing of arrivals," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 163-198, October.
    10. Bountali, Olga & Economou, Antonis, 2017. "Equilibrium joining strategies in batch service queueing systems," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1142-1151.
    11. Sakuma, Yutaka & Masuyama, Hiroyuki & Fukuda, Emiko, 2020. "A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 253-264.
    12. Olga Bountali & Apostolos Burnetas & Lerzan Örmeci, 2022. "Join, balk, or jettison? The effect of flexibility and ranking knowledge in systems with batch arrivals," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3505-3524, September.
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