Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T00:33:22.803Z Has data issue: false hasContentIssue false
  • English
  • Français

On stochastic scheduling with precedence relations and switching costs

Published online by Cambridge University Press:  14 July 2016

K. D. Glazebrook
K. D. Glazebrook*
Affiliation:
University of Newcastle upon Tyne
*
∗Postal address: Department of Statistics, School of Mathematics, The University, Newcastle upon Tyne, NE1 7RU, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

A collection of jobs is to be processed by a single machine. The amount of processing required by each job is a random variable with a known probability distribution. The jobs must be processed in a manner which is consistent with a precedence relation but the machine is free to switch from one job to another at any time; such switches are costly, however. This paper discusses conditions under which there is an optimal strategy for allocating the machine to the jobs which is given by a fixed permutation of the jobs indicating in which order they should be processed. When this is so, existing algorithms may be helpful in giving the best job ordering.

Keywords

MARKOV DECISION PROCESSESSTOCHASTIC SCHEDULINGSWITCHING COSTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1016 - 1024
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bruno, J. and Hofri, M. (1975) On scheduling chains of jobs on one processor with limited preemption. SIAM J. Comput. 4, 478–490.CrossRefGoogle Scholar
Glazebrook, K. D. (1976) Stochastic scheduling with order constraints. Internat. J. Systems Sci. 7, 657–666.CrossRefGoogle Scholar
Glazebrook, K. D. and Gittins, J. C. (1981) On single-machine scheduling with precedence relations and linear or discounted costs. Operat. Res. To appear.CrossRefGoogle Scholar
Meilijson, I. and Weiss, G. (1977) Multiple feedback at a single server station. Stoch. Proc. Appl. 5, 195–205.CrossRefGoogle Scholar
Nash, P. and Gittins, J. C. (1977) A Hamiltonian approach to optimal stochastic resource allocation. Adv. Appl. Prob. 9, 55–68.CrossRefGoogle Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Sidney, J. B. (1975) Decomposition algorithms for single-machine sequencing with precedence relations and deferral costs. Operat. Res. 23, 283–298.CrossRefGoogle Scholar