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Scheduling jobs with exponential processing times on parallel machines

Published online by Cambridge University Press:  14 July 2016

Tapani Lehtonen
Tapani Lehtonen*
Affiliation:
Helsinki School of Economics
*
∗Postal address: Helsinki School of Economics, Runebergink. 22–24, 00100 Helsinki, Finland.
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Abstract

We consider a system where jobs are processed by parallel machines. The processing times are exponentially distributed. An essential feature is that the assignment of the jobs to the machines is decided before the system starts to work. We consider both the flow time and the makespan. In the case of the flow time we allow both the machines and the jobs to be non-homogeneous. The optimization is by minimizing the flow time in the sense of stochastic order and the optimal assignment is obtained for this case. The case of the makespan is harder. We consider the expected makespan and as a partial solution we prove an optimality result for the case where there are two non-homogeneous machines and the jobs are homogeneous. It turns out that the optimal assignment can be expressed by using a quantile of a binomial distribution.

Keywords

SCHEDULINGEXPONENTIAL DISTRIBUTIONFLOW TIMEMAKESPANSTOCHASTIC ORDER
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 752 - 762
Copyright
Copyright © Applied Probability Trust 1988 

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References

Coffman, E. G., Flatto, L., Garey, M. R. and Weber, R. R. (1987) Minimizing expected makespans on uniform processor systems. Adv. Appl. Prob. 19, 177–201.Google Scholar
Lehtonen, T. (1987) A note on the comparison of two sums of exponentially distributed random variables. Research Report D-100, Helsinki School of Economics.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and its Applications. Academic Press, New York.Google Scholar
Pinedo, M. and Weiss, G. (1985) Scheduling jobs with exponentially distributed processing times and intree precedence constraints on two parallel machines. Operat. Res. 33, 1381–1388.Google Scholar
Weber, R. R. (1982) Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flowtime. J. Appl. Prob. 19, 167–182.Google Scholar
Weber, R. R., Varaiya, P. and Walrand, J. (1986) Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. J. Appl. Prob. 23, 841–847.Google Scholar
Weiss, G. and Pinedo, M. (1980) Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. J. Appl. Prob. 17, 187–202.Google Scholar