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Scheduling jobs by stochastic processing requirements on parallel machines to minimize makespan or flowtime

Published online by Cambridge University Press:  14 July 2016

Richard R. Weber
Richard R. Weber*
Affiliation:
University of Cambridge
*
∗Postal address: Queens' College, Cambridge CB3 9ET, U.K.
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Abstract

A number of identical machines operating in parallel are to be used to complete the processing of a collection of jobs so as to minimize either the jobs' makespan or flowtime. The total processing required to complete each job has the same probability distribution, but some jobs may have received differing amounts of processing prior to the start. When the distribution has a monotone hazard rate the expected value of the makespan (flowtime) is minimized by a strategy which always processes those jobs with the least (greatest) hazard rates. When the distribution has a density whose logarithm is concave or convex these strategies minimize the makespan and flowtime in distribution. These results are also true when the processing requirements are distributed as exponential random variables with different parameters.

Keywords

DYNAMIC PROGRAMMINGFLOWTIMEMAKESPANMONOTONE HAZARD RATEOPTIMAL CONTROLSIGN-CONSISTENT FREQUENCYSTOCHASTIC SCHEDULING
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 167 - 182
Copyright
Copyright © Applied Probability Trust 1982 

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