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On the optimality of LEPT and rules for machines in parallel

  • Cheng-Shang Chang (a1), Xiuli Chao (a2), Michael Pinedo (a3) and Richard Weber (a4)

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 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 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.

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Corresponding author

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

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References

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