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On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

Gideon Weiss
Gideon Weiss*
Affiliation:
Georgia Tech
*
* Present address: Department of Statistics, The University of Haifa, Haifa 31905, Israel.
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Abstract

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

Keywords

STOCHASTIC PROCESSING TIMESHOLDING COSTSGITTINS PRIORITY RULE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B35: Scheduling theory, deterministic 90C40: Markov and semi-Markov decision processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 821 - 839
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by NSF grants DDM-8914863 and DDM-9215233, and the fund for the promotion of research at the Technion.

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