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Coordination mechanisms for parallel machine scheduling

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  • Lee, Kangbok
  • Leung, Joseph Y.-T.
  • Pinedo, Michael L.

Abstract

We consider coordination mechanisms for the distributed scheduling of n jobs on m parallel machines, where each agent holding a job selects a machine to process his/her own job. Without a central authority to construct a schedule, each agent acts selfishly to minimize his/her own disutility, which is either the completion time of the job or the congestion time (defined as the load of the machine on which the job is scheduled). However, the overall system performance is measured by a central objective which is quite different from the agents’ objective. In the literature, makespan is often considered as the central objective. We, however, investigate problems with other central objectives that minimize the total congestion time, the total completion time, the maximum tardiness, the total tardiness, and the number of tardy jobs. The performance deterioration of the central objective by a lack of central coordination, referred to as the price of anarchy, is typically measured by the maximum ratio of the objective function value of a Nash equilibrium schedule versus that of an optimal, coordinated schedule. In this paper we give bounds for the price of anarchy for the above objectives. For problems with due date related objectives, the price of anarchy may not be defined since the optimal value may be zero. In this case, we consider the maximum difference between the objective function value of an equilibrium schedule and the optimal value. We refer to this metric as the absolute price of anarchy and analyze its lower and upper bounds.

Suggested Citation

  • Lee, Kangbok & Leung, Joseph Y.-T. & Pinedo, Michael L., 2012. "Coordination mechanisms for parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 220(2), pages 305-313.
  • Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:305-313
    DOI: 10.1016/j.ejor.2012.02.001
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    References listed on IDEAS

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    1. Petra Schuurman & Tjark Vredeveld, 2007. "Performance Guarantees of Local Search for Multiprocessor Scheduling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 52-63, February.
    2. Averbakh, Igor, 2010. "Nash equilibria in competitive project scheduling," European Journal of Operational Research, Elsevier, vol. 205(3), pages 552-556, September.
    3. Rzadca, Krzysztof & Trystram, Denis, 2009. "Promoting cooperation in selfish computational grids," European Journal of Operational Research, Elsevier, vol. 199(3), pages 647-657, December.
    4. Heydenreich, B. & Müller, R.J. & Uetz, M.J., 2006. "Games and mechanism design in machine scheduling - an introduction," Research Memorandum 022, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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    Cited by:

    1. 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.
    2. Felipe T. Muñoz & Rodrigo Linfati, 2024. "Bounding the Price of Anarchy of Weighted Shortest Processing Time Policy on Uniform Parallel Machines," Mathematics, MDPI, vol. 12(14), pages 1-12, July.
    3. Herbert Hamers & Flip Klijn & Marco Slikker, 2019. "Implementation of optimal schedules in outsourcing with identical suppliers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 173-187, April.
    4. 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.
    5. Lee, Kangbok & Leung, Joseph Y-T. & Jia, Zhao-hong & Li, Wenhua & Pinedo, Michael L. & Lin, Bertrand M.T., 2014. "Fast approximation algorithms for bi-criteria scheduling with machine assignment costs," European Journal of Operational Research, Elsevier, vol. 238(1), pages 54-64.
    6. Briskorn, Dirk & Waldherr, Stefan, 2022. "Anarchy in the UJ: Coordination mechanisms for minimizing the number of late jobs," European Journal of Operational Research, Elsevier, vol. 301(3), pages 815-827.

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