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Stability and fairness in the job scheduling problem

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  • Bahel, Eric
  • Trudeau, Christian

Abstract

The job scheduling problem is a classic operations research problem in which agents have jobs to be executed by machines in given time slots, with each machine being able to process only one job at a time. We study this problem using cooperative game theory, focusing on how to divide the minimum cost (of executing all jobs) between the agents. First, we characterize the set of stable allocations, which all charge only users whose jobs are executed in peak-demand time periods. Second, we introduce a number of natural properties that allow to split the cost in a fair and consistent way. Using these desirable properties, we offer axiomatizations for two cost sharing methods that stand out: the peak-demand rule and the peak-interval rule.

Suggested Citation

  • Bahel, Eric & Trudeau, Christian, 2019. "Stability and fairness in the job scheduling problem," Games and Economic Behavior, Elsevier, vol. 117(C), pages 1-14.
    • Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:1-14
    DOI: 10.1016/j.geb.2019.06.006
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    Cited by:

    1. Eric Bahel & Christian Trudeau, 2022. "Minimum coloring problems with weakly perfect graphs," Review of Economic Design, Springer;Society for Economic Design, vol. 26(2), pages 211-231, June.
    2. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2023. "Broadcasting revenue sharing after cancelling sports competitions," Annals of Operations Research, Springer, vol. 328(2), pages 1213-1238, September.
    3. Streekstra, Leanne & Trudeau, Christian, 2020. "Stable source connection and assignment problems as multi-period shortest path problems," Discussion Papers on Economics 7/2020, University of Southern Denmark, Department of Economics.
    4. Matteo Avolio, 2023. "Balancing the Average Weighted Completion Times in Large-Scale Two-Agent Scheduling Problems: An Evolutionary-Type Computational Study," Mathematics, MDPI, vol. 11(19), pages 1-15, September.
    5. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    6. Ata Atay & Christian Trudeau, 2022. "Queueing games with an endogenous number of machines," Working Papers 2202, University of Windsor, Department of Economics.
    7. Gudmundsson, Jens & Hougaard, Jens Leth & Platz, Trine Tornøe, 2023. "Decentralized task coordination," European Journal of Operational Research, Elsevier, vol. 304(2), pages 851-864.
    8. Eric Bahel & Christian Trudeau, 2021. "Minimum coloring problem: the core and beyond," Working Papers 2005, University of Windsor, Department of Economics.

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    More about this item

    Keywords

    Game theory; Cost sharing; Job scheduling; Stability;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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