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Coordination mechanisms for scheduling games with proportional deterioration

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  • Chen, Qianqian
  • Lin, Ling
  • Tan, Zhiyi
  • Yan, Yujie

Abstract

We study parallel-machine scheduling games with deteriorating jobs. The processing time of a job increases proportionally with its starting time by a positive deterioration rate. Each job acts selfishly aiming to minimize its completion time while choosing a machine on which it will be processed. Machines are equipped with coordination mechanisms to diminish chaos caused by jobs’ competition. We consider three coordination mechanisms in this paper, namely Smallest Deterioration Rate first, Largest Deterioration Rate first and MAKESPAN policy. Under these mechanisms, we precisely quantify the inefficiency of their Nash Equilibriums by investigating the Price of Anarchy (PoA) and the Price of Stability (PoS), concerning minimization of social costs including the makespan and the total machine load. By using some new methods, we obtain parametrical bounds on the PoA and PoS, and demonstrate that most of these bounds are tight.

Suggested Citation

  • Chen, Qianqian & Lin, Ling & Tan, Zhiyi & Yan, Yujie, 2017. "Coordination mechanisms for scheduling games with proportional deterioration," European Journal of Operational Research, Elsevier, vol. 263(2), pages 380-389.
    • Handle: RePEc:eee:ejores:v:263:y:2017:i:2:p:380-389
    DOI: 10.1016/j.ejor.2017.05.021
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    References listed on IDEAS

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    1. Yossi Azar & Lisa Fleischer & Kamal Jain & Vahab Mirrokni & Zoya Svitkina, 2015. "Optimal Coordination Mechanisms for Unrelated Machine Scheduling," Operations Research, INFORMS, vol. 63(3), pages 489-500, June.
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    5. Cheng, Mingbao & Tadikamalla, Pandu R. & Shang, Jennifer & Zhang, Shaqing, 2014. "Bicriteria hierarchical optimization of two-machine flow shop scheduling problem with time-dependent deteriorating jobs," European Journal of Operational Research, Elsevier, vol. 234(3), pages 650-657.
    6. Lalla-Ruiz, Eduardo & Voß, Stefan, 2016. "Modeling the Parallel Machine Scheduling Problem with Step Deteriorating Jobs," European Journal of Operational Research, Elsevier, vol. 255(1), pages 21-33.
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    Cited by:

    1. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.
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    3. Braat, Jac & Hamers, Herbert & Klijn, Flip & Slikker, Marco, 2019. "A selfish allocation heuristic in scheduling: Equilibrium and inefficiency bound analysis," European Journal of Operational Research, Elsevier, vol. 273(2), pages 634-645.
    4. Ercan Şenyiğit & Uğur Atici & Mehmet Burak Şenol, 2022. "Effects of OCRA parameters and learning rate on machine scheduling," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 941-959, September.
    5. Cong Chen & Yinfeng Xu, 0. "Coordination mechanisms for scheduling selfish jobs with favorite machines," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-33.
    6. Cong Chen & Yinfeng Xu, 2020. "Coordination mechanisms for scheduling selfish jobs with favorite machines," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 333-365, August.

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