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Loading and Sequencing on Parallel Machines

Published online by Cambridge University Press:  27 July 2009

Rhonda Righter
Rhonda Righter
Affiliation:
Department of Decision and In formation Sciences Santa Clara University Santa Clara, California 95053
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Abstract

We consider the problem of scheduling jobs on parallel machines to minimize flowtime, where all decisions about loading and sequencing must be made before any processing is done. We find policies that minimize flowtime stochastically or in the increasing convex sense under various assumptions.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 2 , April 1992 , pp. 193 - 199
Copyright
Copyright © Cambridge University Press 1992

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References

Brown, M. & Solomon, H. (1973). Optimal issuing policies under stochastic field lives. Journal of Applied Probability 10: 761–768.CrossRefGoogle Scholar
Chang, C.-S. & Yao, D.D. (1990). Rearrangement, majorization and stochastic scheduling. Preprint.Google Scholar
Glazebrook, K.D. (1979). Scheduling tasks with exponential service times on parallel processors. Journal of Applied Probability 16: 685–689.CrossRefGoogle Scholar
Lawler, E.L. (1973). Optimal sequencing of a single machine subject to precedence constraints. Management Science 10: 544–546.CrossRefGoogle Scholar
Lehtonen, T. (1988). Scheduling jobs with exponential processing times on parallel machines. Journal of Applied Probability 25: 752–762.CrossRefGoogle Scholar
Pinedo, M. (1983). Stochastic scheduling with release dates and due dates. Operations Research 31: 599–572.CrossRefGoogle Scholar
Righter, R. & Xu, S. (1991). Scheduling jobs on nonidentical IFR processors to minimize general cost functions. Advances of Applied Probability 23: 193–199.CrossRefGoogle Scholar
Ross, S.M. (1983). Stochastic dynamic programming. New York:Wiley.Google Scholar
Ross, S.M. (1983). Stochastic processes. New York: Wiley.Google Scholar
Shanthikumar, J.G. & Yao, D.D. (1991). Bivariate characterization of some stochastic order relations. Advances in Applied Probability 23: 642–659.CrossRefGoogle Scholar
Weber, R.R. (1982). Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flowtime. Journal of Applied Probability 19: 167–182.CrossRefGoogle Scholar
Weber, R.R., Varaiya, P., & Walrand, J. (1986). Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. Journal of Applied Probability 23: 841–847.CrossRefGoogle Scholar
Weiss, G. (1984). Scheduling spares with exponential lifetimes in a two-component parallel system. Naval Research Logistics Quarterly 31: 431–446.CrossRefGoogle Scholar
Weiss, G. & Pinedo, M. (1980). Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. Journal ofApplied Probability 17: 187–202.Google Scholar
Xu, S. (1992). Socially and individually optimal routing of stochastic jobs in parallel processor systems. Operations Research (to appear).CrossRefGoogle Scholar
Xu, S.H. (1991). Stochastically minimizing total delay of jobs subject to random deadlines. Probability in the Engineering and Informational Sciences 5: 333–348.CrossRefGoogle Scholar