Decentralization and Mechanism Design for Online Machine Scheduling

  • Birgit Heydenreich
  • Rudolf Müller
  • Marc Uetz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)


We study the online version of the classical parallel machine scheduling problem to minimize the total weighted completion time from a new perspective: We assume that the data of each job, namely its release date r j , its processing time p j and its weight w j is only known to the job itself, but not to the system. Furthermore, we assume a decentralized setting where jobs choose the machine on which they want to be processed themselves. We study this problem from the perspective of algorithmic mechanism design. We introduce the concept of a myopic best response equilibrium, a concept weaker than the dominant strategy equilibrium, but appropriate for online problems. We present a polynomial time, online scheduling mechanism that, assuming rational behavior of jobs, results in an equilibrium schedule that is 3.281-competitive. The mechanism deploys an online payment scheme that induces rational jobs to truthfully report their private data. We also show that the underlying local scheduling policy cannot be extended to a mechanism where truthful reports constitute a dominant strategy equilibrium.


Completion Time Competitive Ratio Payment Scheme Online Schedule Total Weighted Completion Time 


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  1. 1.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discr. Math. 5, 287–326 (1979)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Lenstra, J.K., Rinnoy Kan, A.H.G., Brucker, P.: Complexity of machine scheduling problems. Ann. of Discr. Math. 1, 343–362 (1977)CrossRefGoogle Scholar
  3. 3.
    Hoogeveen, J.A., Vestjens, A.P.A.: Optimal on-line algorithms for single machine scheduling. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, pp. 404–414. Springer, Heidelberg (1996)Google Scholar
  4. 4.
    Vestjens, A.P.A.: On-line Machine Scheduling. PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands (1997)Google Scholar
  5. 5.
    Anderson, E.J., Potts, C.N.: Online scheduling of a single machine to minimize total weighted completion time. Math. Oper. Res. 29, 686–697 (2004)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Correa, J.R., Wagner, M.R.: LP-based online scheduling: from single to parallel machines. In: Jünger, M., Kaibel, V. (eds.) IPCO 2005. LNCS, vol. 3509, pp. 196–209. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Megow, N., Schulz, A.S.: On-line scheduling to minimize average completion time revisited. Oper. Res. Letters 32, 485–490 (2004)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Megow, N., Uetz, M., Vredeveld, T.: Models and algorithms for stochastic online scheduling. Math. Oper. Res. (to appear)Google Scholar
  9. 9.
    Smith, W.: Various optimizers for single stage production. Nav. Res. Log. Quarterly 3, 59–66 (1956)CrossRefGoogle Scholar
  10. 10.
    Nisan, N., Ronen, A.: Algorithmic mechanism design. Games and Economic Behavior 35, 166–196 (2001)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Archer, A., Tardos, E.: Truthful mechanisms for one-parameter agents. In: Proc. 42nd FOCS, pp. 482–491. IEEE Computer Society Press, Los Alamitos (2001)Google Scholar
  12. 12.
    Kovacs, A.: Fast monotone 3-approximation algorithm for scheduling related machines. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 616–627. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Porter, R.: Mechanism design for online real-time scheduling. In: Proc. 5th ACM Conf. Electronic Commerce, pp. 61–70. ACM Press, New York (2004)CrossRefGoogle Scholar
  14. 14.
    Eastman, W.L., Even, S., Isaacs, I.M.: Bounds for the optimal scheduling of n jobs on m processors. Management Science 11, 268–279 (1964)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Lavi, R., Mu’alem, A., Nisan, N.: Towards a characterization of truthful combinatorial auctions. In: Proc. 44th FOCS, pp. 574–583. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Birgit Heydenreich
    • 1
  • Rudolf Müller
    • 1
  • Marc Uetz
    • 1
  1. 1.Quantitative EconomicsMaastricht UniversityMaastrichtThe Netherlands

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