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Price of fairness in two-agent single-machine scheduling problems

Author

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  • Agnetis, Alessandro
  • Chen, Bo
  • Nicosia, Gaia
  • Pacifici, Andrea

Abstract

We investigate the concept of price of fairness in resource allocation and apply it to two-agent single-machine scheduling problems, in which two agents, each having a set of jobs, compete for use of a single machine to execute their jobs. We consider the situation where one agent aims at minimizing the total of the completion times of his jobs, while the other seeks to minimize the maximum tardiness with respect to a common due date for her jobs. We first explore and propose a definition of utility, then we study both max-min and proportionally fair solutions, providing a tight bound on the price of fairness for each notion of fairness. We extend our study further to the problem in which both agents wish to minimize the total of the completion times of their own jobs.

Suggested Citation

  • Agnetis, Alessandro & Chen, Bo & Nicosia, Gaia & Pacifici, Andrea, 2019. "Price of fairness in two-agent single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 276(1), pages 79-87.
    • Handle: RePEc:eee:ejores:v:276:y:2019:i:1:p:79-87
    DOI: 10.1016/j.ejor.2018.12.048
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    Cited by:

    1. Zhang, Xingong, 2021. "Two competitive agents to minimize the weighted total late work and the total completion time," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    2. Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy & Julia Resch & Giovanni Righini, 2021. "Optimally rescheduling jobs with a Last-In-First-Out buffer," Journal of Scheduling, Springer, vol. 24(6), pages 663-680, December.
    3. Aziz, Haris & Huang, Xin & Mattei, Nicholas & Segal-Halevi, Erel, 2023. "Computing welfare-Maximizing fair allocations of indivisible goods," European Journal of Operational Research, Elsevier, vol. 307(2), pages 773-784.
    4. Ruyan He & Jinjiang Yuan, 2020. "Two-Agent Preemptive Pareto-Scheduling to Minimize Late Work and Other Criteria," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    5. Shi-Sheng Li & Ren-Xia Chen, 2023. "Competitive two-agent scheduling with release dates and preemption on a single machine," Journal of Scheduling, Springer, vol. 26(3), pages 227-249, June.
    6. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    7. 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.
    8. Gudmundsson, Jens & Hougaard, Jens Leth & Platz, Trine Tornøe, 2023. "Decentralized task coordination," European Journal of Operational Research, Elsevier, vol. 304(2), pages 851-864.
    9. Jiang, Yanmin & Wu, Xiaole & Chen, Bo & Hu, Qiying, 2021. "Rawlsian fairness in push and pull supply chains," European Journal of Operational Research, Elsevier, vol. 291(1), pages 194-205.

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