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On the optimality of LEPT and cµ rules for machines in parallel

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Cheng-Shang Chang ,
Xiuli Chao ,
Michael Pinedo  and
Richard Weber
Cheng-Shang Chang*
Affiliation:
T. J. Watson Research Center
Xiuli Chao*
Affiliation:
New Jersey Institute of Technology
Michael Pinedo*
Affiliation:
Columbia University
Richard Weber*
Affiliation:
University of Cambridge
*
∗Postal address: IBM Research Division, T.J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA.
∗∗Postal address: Division of Industrial and Management Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA.
∗∗∗Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA.
∗∗∗∗Postal address: Cambridge University Engineering Department, Mill Lane, Cambridge, CB2 1RX, UK.
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Abstract

We consider scheduling problems with m machines in parallel and n jobs. The machines are subject to breakdown and repair. Jobs have exponentially distributed processing times and possibly random release dates. For cost functions that only depend on the set of uncompleted jobs at time t we provide necessary and sufficient conditions for the LEPT rule to minimize the expected cost at all t within the class of preemptive policies. This encompasses results that are known for makespan, and provides new results for the work remaining at time t. An application is that if the cµ rule has the same priority assignment as the LEPT rule then it minimizes the expected weighted number of jobs in the system for all t. Given appropriate conditions, we also show that the cµ rule minimizes the expected value of other objective functions, such as weighted sum of job completion times, weighted number of late jobs, or weighted sum of job tardinesses, when jobs have a common random due date.

Keywords

EXPONENTIAL DISTRIBUTIONMAKESPANPRIORITY POLICIESSTOCHASTIC SCHEDULINGWEIGHTED FLOWTIME

MSC classification

Primary: 90B35: Scheduling theory, deterministic
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 667 - 681
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

The research of this author was partially supported by the NSF under grant ECS 86–14689.

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