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Some problems of stochastic resource allocation

Published online by Cambridge University Press:  14 July 2016

J. C. Gittins
J. C. Gittins*
Affiliation:
University Engineering Laboratory, Cambridge
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Abstract

Suppose that a number of jobs are to be carried out by a single processing unit orserver. The server can process any number of jobs at the same time but the time taken to finish all the jobs is the same no matter what scheduling policy is used, provided the server is never left idle. It is, however, possible to minimise the total delays to individual jobs by adopting a suitable policy. Optimal policies are derived here for the situation when the processing times are random variables. If the completion rates (analogous to hazard rates) for every job are increasing it is optimal to process the jobs in sequence. If they are decreasing the optimal policy involves simultaneous processing. These results are applied to a more general resource allocation problem arising in industrial chemical research.

Keywords

RESOURCE ALLOCATIONCHEMICAL RESEARCHTIME SHARINGSTOCHASTIC SCHEDULING
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 360 - 369
Copyright
Copyright © Applied Probability Trust 1972 

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References

Gittins, J. C. (1969) Optimal resource allocation in chemical research. Adv. Appl. Prob. 1, 238–270.Google Scholar
Laska, E., Meisner, M. and Siegel, C. (1972) Contributions to the theory of optimal resource allocation. J. Appl. Prob. 9, 337–359.Google Scholar
Kamien, M. I. and Schwartz, N. L. (1971) Expenditure patterns for risky R and D projects. J. Appl. Prob. 8, 60–73.CrossRefGoogle Scholar