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The Stochastic Optimality of SEPT in Parallel Machine Scheduling

Published online by Cambridge University Press:  27 July 2009

Cheng-Shang Chang ,
Arie Hordijk ,
Rhonda Righter  and
Gideon Weiss
Cheng-Shang Chang
Affiliation:
IBM Research Division, T. J. Watson Research Center, P.O. Box 704, Yorktown Heights, New York 10598
Arie Hordijk
Affiliation:
Institute of Applied Mathematics and Computer Science, University of Leiden, P.O. Box 9512, 2333 CA Leiden, The Netherlands
Rhonda Righter
Affiliation:
Department of Decision and Information Sciences, Santa Clara University, Santa Clara, California 95053
Gideon Weiss
Affiliation:
Faculty of Industrial Engineering and Management, The Technion, Technion City, Haifa 32000, Israel
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Abstract

We consider preemptive scheduling on parallel machines where processing times of jobs are i.i.d. but jobs may already have received distinct amounts of service. We show that when processing times are increasing in likelihood ratio, SEPT (shortest expected [remaining] processing time first) stochastically minimizes any increasing and Schur-concave function of the job completion times. The same result holds when processing times are exponential with possibly different means.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 2 , April 1994 , pp. 179 - 188
Copyright
Copyright © Cambridge University Press 1994

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