Rearrangement, majorization and stochastic scheduling
Mathematics of Operations Research
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
Approximation in stochastic scheduling: the power of LP-based priority policies
Journal of the ACM (JACM)
A Supermodular Relaxation for Scheduling with Release Dates
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Models and Algorithms for Stochastic Online Scheduling
Mathematics of Operations Research
Approximation in preemptive stochastic online scheduling
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Stochastic Online Scheduling Revisited
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Active Scheduling of Organ Detection and Segmentation in Whole-Body Medical Images
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Scheduling shared scans of large data files
Proceedings of the VLDB Endowment
Preemptive stochastic online scheduling on two uniform machines
Information Processing Letters
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We consider the stochastic single-machine problem, when the objective is to minimize the expected total weighted completion time of a set of jobs that are released over time. We assume that the existence and the parameters of each job including its release date, weight, and expected processing times are not known until its release date. The actual processing times are not known until processing is completed. We analyze the performance of the on-line nonpreemptive weighted shortest expected processing time among available jobs (WSEPTA) heuristic. When a scheduling decision needs to be made, this heuristic assigns, among the jobs that have arrived but not yet processed, one with the largest ratio of its weight to its expected processing time. We prove that when the job weights and processing times are bounded and job processing times are mutually independent random variables, WSEPTA is asymptotically optimal for the single-machine problem. This implies that WSEPTA generates a solution whose relative error approaches zero as the number of jobs increases. This result can be extended to the stochastic flow shop and open shop problems, as well as models with stochastic job weights.