Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines (original) (raw)

Abstract

We study the stochastic online scheduling on m uniform machines with the objective to minimize the expected value of total weighted completion times of a set of jobs that arrive over time. For each job, the processing time is a random variable, and the distribution of processing time is unknown in advance. The actual processing time could be known only when the job is completed. For the problem, we propose a policy which is proved to be asymptotically optimal when the processing times and weights are uniformly bounded, i.e. the relative error of the solution achieved by our policy approaches zero as the number of jobs increases to infinity.

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References

• Chen, G., & Shen, Z. M. (2007). Probabilistic analysis of stochastic online scheduling problems. IIE Transactions, 39, 525–538.
  Article Google Scholar
• Chou, M., Liu, H., Queyranne, M., et al. (2006a). On the asymptotic optimality of a simple on-line algorithm for the stochastic single-machine weighted completion time problem and its extensions. Operations Research, 54, 464–474.
  Article Google Scholar
• Chou, M., Queyranne, M., & Simchi-Levi, D. (2006b). The asymptotic performance ratio of an on-line algorithm for uniform parallel machine scheduling with release dates. Mathematical Programming, 106, 137–157.
  Article Google Scholar
• Correa, J. R., & Wagner, M. R. (2009). LP-based online scheduling: from single to parallel machines. Mathematical Programming, 119(1), 109–136.
  Article Google Scholar
• Goemans, M. X. (1996). A supermodular relaxation for scheduling with release dates. In Lecture notes in computer science: Vol. 1084. Proc. 5th integer programming and combinatorial optimization conference (pp. 288–300). Berlin: Springer.
  Google Scholar
• Goemans, M. X. (1997). Improved approximation algorithms for scheduling with release dates. In Proceedings of the eighth annual ACM-SIAM symposium on discrete algorithms (pp. 591–598). Philadelphia: SZAM.
  Google Scholar
• Goemans, M. X., Queyranne, M., Schulz, A. S., et al. (2002). Single machine scheduling with release dates. SIAM Journal on Discrete Mathematics, 15, 165–192.
  Article Google Scholar
• Liu, H., Queyranne, M., & Simchi-Levi, D. (2005). On the asymptotic optimality of algorithms for the flow shop problem with release dates. Naval Research Logistics, 52, 232–242.
  Article Google Scholar
• Megow, N., Uetz, M., & Vredeveld, T. (2006). Models and algorithms for stochastic online scheduling. Mathematics of Operations Research, 31, 513–525.
  Article Google Scholar
• Möhring, R. H., Schulz, A. S., & Uetz, M. (1999). Approximation in stochastic scheduling: the power of LP-based priority policies. Journal of the ACM, 46, 924–942.
  Article Google Scholar
• Schulz, A. S. (1996). Scheduling to minimize total weighted completion time: performance guarantees of LP-based heuristics and lower bounds. In Proceedings of the 5th international IPCO conference on integer programming and combinatorial optimization (pp. 301–315).
  Google Scholar
• Skutella, M., & Uetz, M. (2005). Stochastic machine scheduling with precedence constraints. SIAM Journal on Computing, 34, 788–802.
  Article Google Scholar
• Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3, 59–66.
  Article Google Scholar

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Authors and Affiliations

1. Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, China
   Manzhan Gu
2. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China
   Xiwen Lu

Authors

1. Manzhan Gu
2. Xiwen Lu

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Correspondence toXiwen Lu.

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Gu, M., Lu, X. Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines.Ann Oper Res 191, 97–113 (2011). https://doi.org/10.1007/s10479-011-0985-1

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• Published: 08 October 2011
• Issue date: November 2011
• DOI: https://doi.org/10.1007/s10479-011-0985-1

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