Skip to main content Accessibility help
×
Home

On the undiscounted tax problem with precedence constraints

  • K. D. Glazebrook (a1)

Abstract

A single machine is available to process a collection of jobs J, each of which evolves stochastically under processing. Jobs incur costs while awaiting the machine at a rate which is state dependent and processing must respect a set of precedence constraints Γ. Index policies are optimal in a variety of scenarios. The indices concerned are characterised as values of restart problems with the average reward criterion. This characterisation yields a range of efficient approaches to their computation. Index-based suboptimality bounds are derived for general processing policies. These bounds enable us to develop sensitivity analyses and to evaluate scheduling heuristics.

Copyright

Corresponding author

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

References

Hide All
Bertsimas, D. and Niño-Mora, J. (1994) Conservation laws, extended polymatroids and multi-armed bandit problems: a unified approach to indexable systems. Unpublished manuscript.
Gittins, J. C. (1989) Multi-Armed Bandit Allocation Indices. Wiley, New York.
Glazebrook, K. D. (1976) Stochastic scheduling with order constraints. Int. J. Systems Sci. 7, 657666.
Glazebrook, K. D. (1982) On the evaluation of suboptimal strategies for families of alternative bandit processes. J. Appl. Prob. 19, 716722.
Glazebrook, K. D. (1983) Stochastic scheduling with due dates. Int. J. Systems Sci. 14, 12591271.
Glazebrook, K. D. (1987) Sensitivity analysis for stochastic scheduling problems. Math. Operat. Res. 12, 205223.
Glazebrook, K. D. (1991) Strategy evaluation for stochastic scheduling problems with order constraints. Adv. Appl. Prob. 23, 86104.
Glazebrook, K. D. and Gittins, J. C. (1981) On single-machine scheduling with precedence relations and linear or discounted costs. Operat. Res. 29, 161173.
Katehakis, M. N. and Veinott, A. F. (1987) The multi-armed bandit problem: decomposition and computation. Math. Operat. Res. 12, 262268.
Klimov, G. P. (1974) Time sharing service systems I. Theory Prob. Appl. 19, 532551.
Lai, T. L. and Ying, Z. (1988) Open bandit processes and optimal scheduling of queueing networks. Adv. Appl Prob. 20, 447472.
Nain, P., Tsoucas, P. and Walrand, J. C. (1989) Interchange arguments in stochastic scheduling. J. Appl. Prob. 27, 815826.
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.
Ross, S. M. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, New York.
Sidney, J. B. (1975) Decomposition algorithms for single-machine scheduling with precedence relations and deferral costs. Operat. Res. 23, 283293.
Tijms, H. C. (1986) Stochastic Modelling and Analysis: A Computational Approach.
Tsitsiklis, J. N. (1994) A short proof of the Gittins index theorem. Ann. Appl. Prob. 4, 194199.
Varaiya, P., Walrand, J. C. and Buyukkoc, C. (1985) Extensions of the multiarmed bandit problem: the discounted case. IEEE Trans. Aut. Control. AC–30, 426439.
Walrand, J. C. (1988) An Introduction to Queueing Networks. Prentice Hall, Englewood Cliffs, N.J.

Keywords

MSC classification

Related content

Powered by UNSILO

On the undiscounted tax problem with precedence constraints

  • 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.