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Stochastic scheduling for a two-machine open shop

Part of: Operations research and management science Computer system organization

Published online by Cambridge University Press:  14 July 2016

Rhonda Righter
Rhonda Righter*
Affiliation:
Santa Clara University
*
∗Postal address: Department of Decision and Information Sciences, Santa Clara University, Santa Clara, CA 95053, USA.
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Abstract

We study the problem of preemptive scheduling of jobs in a two-machine open shop. Jobs require processing on both machines, but the order does not matter. We define the D-LERPT (double longest expected remaining processing time) policy as the policy that first processes jobs that have not yet been processed by either machine (double jobs), in decreasing order of expected remaining processing times, and then processes jobs that require processing on only one machine in any order. We show that D-LERPT stochastically minimizes the makespan when preemption is not permitted and jobs (but not machines) are stochastically identical, and that D-LERPT minimizes the makespan in the increasing convex sense when preemption is permitted and the machines are stochastically identical and processing times are exponential or geometric with a job dependent rate.

Keywords

OPEN SHOPMAKESPANSTOCHASTIC SCHEDULINGCOUPLING

MSC classification

Primary: 90B35: Scheduling theory, deterministic
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 733 - 744
Copyright
Copyright © Applied Probability Trust 1997 

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References

Chang, C.-S. and Righter, R. (1994) The optimality of LEPT in parallel machine scheduling. J Appl. Prob. 31, 788–796.Google Scholar
Frostig, E. (1997) On the optimality of static policy in stochastic open shop. Operat. Res. Lett. To appear.Google Scholar
Pinedo, M. (1984) Optimal policies in stochastic shop scheduling. Ann. Operat. Res. 1, 305–329.Google Scholar
Pinedo, M. (1995) Scheduling: Theory, Algorithms, and Systems. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Pinedo, M. and Ross, S. (1982) Minimizing expected makespan in stochastic open shops. Adv. Appl. Prob. 14, 898–911.Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar