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Inequalities and bounds for the scheduling of stochastic jobs on parallel machines

Published online by Cambridge University Press:  14 July 2016

Michael Pinedo  and
Zvi Schechner
Michael Pinedo*
Affiliation:
Columbia University
Zvi Schechner*
Affiliation:
Columbia University
*
Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA.
Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA.
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Abstract

Consider n jobs and m machines. The m machines are identical and set up in parallel. All n jobs are available at t = 0 and each job has to be processed on one of the machines; any one can do. The processing time of job j is Xj, a random variable with distribution Fj. The sequence in which the jobs start with their processing is predetermined and preemptions are not allowed. We investigate the effect of the variability of the processing times on the expected makespan and the expected time to first idleness. Bounds are presented for these quantities in case the distributions of the processing times of the jobs are new better (worse) than used.

Keywords

MAKESPANTIME TO FIRST IDLENESSVARIABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 739 - 744
Copyright
Copyright © Applied Probability Trust 1985 

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