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A strategic model of job arrivals to a single machine with earliness and tardiness penalties

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  • Amihai Glazer
  • Refael Hassin
  • Liron Ravner

Abstract

We consider a game of decentralized timing of jobs to a single server (machine) with a penalty for deviation from a due date, and no delay costs. The jobs’ sizes are homogeneous and deterministic. Each job belongs to a single decision maker, a customer, who aims to arrive at a time that minimizes his(her) deviation penalty. If multiple customers arrive at the same time, then their order of service is determined by a uniform random draw. We show that if the cost function has a weighted absolute deviation form, then any Nash equilibrium is pure and symmetric, that is, all customers arrive together. Furthermore, we show that there exist multiple, in fact a continuum, of equilibrium arrival times, and provide necessary and sufficient conditions for the socially optimal arrival time to be an equilibrium. The base model is solved explicitly, but the prevalence of a pure symmetric equilibrium is shown to be robust to several relaxations of the assumptions: restricted server availability, inclusion of small waiting costs, stochastic job sizes, randomly sized population, heterogeneous due dates, and nonlinear deviation penalties.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:uiiexx:v:50:y:2018:i:4:p:265-278
    DOI: 10.1080/24725854.2017.1395098
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    Cited by:

    1. Alexander Matros & Vladimir Smirnov & Andrew Wait, 2024. "Sunk costs, entry and clustering," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(3), pages 747-782, May.
    2. Ghosh, Souvik & Hassin, Refael, 2021. "Inefficiency in stochastic queueing systems with strategic customers," European Journal of Operational Research, Elsevier, vol. 295(1), pages 1-11.
    3. Tzvi Alon & Moshe Haviv, 2023. "Choosing a batch to be processed," Annals of Operations Research, Springer, vol. 326(1), pages 67-87, July.
    4. 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.
    5. Alon, Tzvi & Haviv, Moshe, 2022. "Discrete-time strategic job arrivals to a single machine with waiting and lateness penalties," European Journal of Operational Research, Elsevier, vol. 303(1), pages 480-486.

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