Skip to main content Accessibility help

Strategy evaluation for stochastic scheduling problems with order constraints

  • K. D. Glazebrook (a1)


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.


Corresponding author

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


Hide All

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.



Hide All
Gittins, J. C. (1979) Bandit processes and dynamic allocation indices (with discussion). J. R. Statist. Soc. B41, 148177.
Gittins, J. C. (1989) Multi-armed Bandit Allocation Indices. Wiley, Chichester.
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, 241266.
Glazebrook, K. D. (1976) Stochastic scheduling with order constraints. Int. J. Systems Sci. 7, 657666.
Glazebrook, K. D. (1984) Scheduling stochastic jobs on a single machine subject to breakdowns. Nav. Res. Logist. Quart. 31, 251264.
Glazebrook, K. D. (1987) Sensitivity analysis for stochastic scheduling problems. Math. Operat. Res. 12, 205223.
Glazebrook, K. D. (1990) Procedures for the evaluation of strategies for resource allocation in a stochastic environment. J. Appl. Prob. 27, 215220.
Glazebrook, K. D. and Gittins, J. C. (1981) On single-machine scheduling with precedence relations and linear or discounted costs. Operat. Res. 29, 161173.
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.
Nash, P. (1973) Optimal Allocation of Resources to Research Projects. Ph.D. Thesis, University of Cambridge.
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.
Weber, R. R. (1982) Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flow time. J. Appl. Prob. 19, 167182.
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, 187202.
Whittle, P. (1981) Arm-acquiring bandits. Ann. Prob. 9, 284292.
Whittle, P. (1988) Restless bandits: activity allocation in a changing world. In A Celebration of Applied Probability , J. Appl. Prob. 25A, 287298.


Related content

Powered by UNSILO

Strategy evaluation for stochastic scheduling problems with order constraints

  • K. D. Glazebrook (a1)


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.