Skip to main content Accessibility help
×
Home

On permutation policies for the scheduling of deteriorating stochastic jobs on a single machine

  • K. D. Glazebrook (a1)

Abstract

A single machine is available to process a collection of stochastic jobs. Processing is preemptive and so (for example) the machine is allowed to switch away from a job before completion, should that prove advantageous. The jobs are deteriorating in the sense that their processing requirements grow (at job-specific rates) as they await processing. This phenomenon might be expected to enhance the status of non-preemptive policies. The primary objective of the paper is to find conditions which are sufficient to ensure the existence of a permutation policy to minimise the expected makespan. We also derive results for a weighted flowtime criterion. Applications of such models to the control of queues and to communication systems have been cited by other authors.

Copyright

Corresponding author

Postal address: Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, UK.

References

Hide All
Bertsekas, D. P. (1976) Dynamic Programming and Stochastic Control. Academic Press, New York.
Browne, S. and Yechiali, U. (1990) Scheduling deteriorating jobs on a single processor. Operat. Res. 38, 495498.
Gittins, J. C. (1989) Multi-armed Bandit Allocation Indices. Wiley, New York.
Glazebrook, K. D. (1984) Scheduling stochastic jobs on a single machine subject to breakdowns. Naval. Res. Logist. Quart. 31, 251264.
Glazebrook, K. D. (1987) Evaluating the effects of machine breakdowns in stochastic scheduling problems. Naval. Res. Logist. 34, 319335.
Glazebrook, K. D. (1991) On nonpreemptive policies for stochastic single-machine scheduling with breakdowns. Prob. Eng. Inf. Sci. 5, 7787.
Glazebrook, K. D. (1992) Single machine scheduling of stochastic jobs subject to deterioration or delay. Naval Res. Logist. 39, 613633.
Glazebrook, K. D. and Whitaker, L. R. (1992) Single-machine stochastic scheduling with dependent processing times. Adv. Appl. Prob. 24, 635652.
Hardy, G., Littlewood, J. E. and Pólya, G. (1934) Inequalities. Cambridge University Press.
Lawless, J. F. (1982) Statistical Models and Methods for Lifetime Data. Wiley, New York.
Pinedo, M. (1982) On the computational complexity of stochastic scheduling problems. In Deterministic and Stochastic Scheduling (ed. Dempster, M. A. H., Lenstra, J. K. and Rinnooy Kan, A. H.), pp. 355365, Reidel, Dordrecht.
Righter, R. and Shanthikumar, J. G. (1989) Scheduling multiclass single server queueing systems to stochastically maximise the number of successful departures. Prob. Eng. Inf. Sci. 3, 323333.
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.
Weber, R. R. (1982) Scheduling jobs with stochastic processing requirement on parallel machines to minimise makespan or flowtime. J. Appl. Prob. 19, 167182.
Weiss, G. (1982) Multiserver stochastic scheduling. In Deterministic and Stochastic Scheduling (ed. Dempster, M. A. H., Lenstra, J. K. and Rinnooy Kan, A. H.), pp. 157179, Reidel, Dordrecht.

Keywords

MSC classification

Related content

Powered by UNSILO

On permutation policies for the scheduling of deteriorating stochastic jobs on a single machine

  • K. D. Glazebrook (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.