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Stability and fairness in the job scheduling problem

Author

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  • Eric Bahel

    (Department of Economics, Virginia Polytechnic Institute and State University)

  • Christian Trudeau

    (Department of Economics, University of Windsor)

Abstract

The job scheduling problem is a classic operational 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, using properties designed to avoid strategic mergers or splits of the jobs, we offer axiomatizations for two remarkable stable allocation rules. Third, observing that all stable rules fail Unanimity Lower Bound (ULB), a property requiring that everybody pay an equal share of the first machine (since it is needed by all), we study and axiomatize the Shapley value, which satisfies ULB. A compromise is then proposed between Stability and ULB.

Suggested Citation

  • Eric Bahel & Christian Trudeau, 2018. "Stability and fairness in the job scheduling problem," Working Papers 1803, University of Windsor, Department of Economics.
    • Handle: RePEc:wis:wpaper:1803
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Atay, Ata & Trudeau, Christian, 2024. "Queueing games with an endogenous number of machines," Games and Economic Behavior, Elsevier, vol. 144(C), pages 104-125.
    4. 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.
    5. 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.
    6. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    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; unanimity lower bound; Shapley value.;
    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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