Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T04:21:21.780Z Has data issue: false hasContentIssue false
  • English
  • Français

Strategy evaluation for stochastic scheduling problems with order constraints

Published online by Cambridge University Press:  01 July 2016

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

Abstract

A single machine is available to process a collection J of jobs. The machine is free to switch between jobs at any time, but processing must respect a set Γof precedence constraints. Jobs evolve stochastically and earn rewards as they are processed, not otherwise. The theoretical framework of forwards induction/Gittins indexation is used to develop approaches to strategy evaluation for quite general (J,Γ). The performance of both forwards induction strategies and a class of quasi-myopic heuristics is assessed.

Keywords

FORWARDS INDUCTIONGITTINS INDEXMARKOV DECISION PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 1 , March 1991 , pp. 86 - 104
Copyright
Copyright © Applied Probability Trust 1991 

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.)

Footnotes

During the course of this research, Dr Glazebrook was supported by the National Research Council as a Senior Research Associate at the Department of Operations Research, Naval Postgraduate School, Monterey, CA 93943-5000, USA.

References

Gittins, J. C. (1979) Bandit processes and dynamic allocation indices (with discussion). J. R. Statist. Soc. B41, 148–177.Google Scholar
Gittins, J. C. (1989) Multi-armed Bandit Allocation Indices. Wiley, Chichester.Google Scholar
Gittins, J. C. and Jones, D. M. (1974) A dynamic allocation index for the sequential design of experiments. In Progress in Statistics , ed. Gani, J., North Holland, Amsterdam, 241–266.Google Scholar
Glazebrook, K. D. (1976) Stochastic scheduling with order constraints. Int. J. Systems Sci. 7, 657–666.Google Scholar
Glazebrook, K. D. (1984) Scheduling stochastic jobs on a single machine subject to breakdowns. Nav. Res. Logist. Quart. 31, 251–264.CrossRefGoogle Scholar
Glazebrook, K. D. (1987) Sensitivity analysis for stochastic scheduling problems. Math. Operat. Res. 12, 205–223.Google Scholar
Glazebrook, K. D. (1990) Procedures for the evaluation of strategies for resource allocation in a stochastic environment. J. Appl. Prob. 27, 215–220.Google Scholar
Glazebrook, K. D. and Gittins, J. C. (1981) On single-machine scheduling with precedence relations and linear or discounted costs. Operat. Res. 29, 161–173.Google Scholar
Glazebrook, K. D., Boys, R. J., and Fay, N. A. (1989) On the evaluation of strategies for branching bandit processes. Ann. Operat. Res. To appear.Google Scholar
Nash, P. (1973) Optimal Allocation of Resources to Research Projects. Ph.D. Thesis, University of Cambridge.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Weber, R. R. (1982) Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flow time. J. Appl. Prob. 19, 167–182.CrossRefGoogle Scholar
Weiss, G. and Pinedo, M. (1980) Scheduling tasks with exponential service time on non-identical processors to minimize various cost functions. J. Appl. Prob. 17, 187–202.CrossRefGoogle Scholar
Whittle, P. (1981) Arm-acquiring bandits. Ann. Prob. 9, 284–292.Google Scholar
Whittle, P. (1988) Restless bandits: activity allocation in a changing world. In A Celebration of Applied Probability , J. Appl. Prob. 25A, 287–298.Google Scholar