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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen, G., & Shen, Z. M. (2007). Probabilistic analysis of stochastic online scheduling problems. IIE Transactions, 39, 525–538.
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.
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.
Correa, J. R., & Wagner, M. R. (2009). LP-based online scheduling: from single to parallel machines. Mathematical Programming, 119(1), 109–136.
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.
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.
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.
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.
Megow, N., Uetz, M., & Vredeveld, T. (2006). Models and algorithms for stochastic online scheduling. Mathematics of Operations Research, 31, 513–525.
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.
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).
Skutella, M., & Uetz, M. (2005). Stochastic machine scheduling with precedence constraints. SIAM Journal on Computing, 34, 788–802.
Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3, 59–66.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-011-0985-1