Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T07:12:34.165Z Has data issue: false hasContentIssue false
  • English
  • Français

On the scheduling of alternative stochastic jobs on a single machine

Published online by Cambridge University Press:  01 July 2016

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

Abstract

Standard models in stochastic resource allocation concern the economic processing of all jobs in some set J. We consider a set up in which tasks in various subsets of J are deemed to be alternative to one another, in that only one member of such a subset of alternative tasks will be completed during the evolution of the process. Existing stochastic scheduling methodology for single-machine problems is developed and extended to this novel class of models. A major area of application is in research planning.

Keywords

ALTERNATIVE TASKSGITTINS INDEXNON-PREEMPTIVE STRATEGYSUPERPROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 955 - 973
Copyright
Copyright © Applied Probability Trust 1987 

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

Bergman, S. W. and Gittins, J. C. (1985) Statistical Methods for Pharmaceutical Research Planning. Marcel Dekker, New York.Google Scholar
Bruno, J. and Hofri, M. (1975) On scheduling chains of jobs on one processor with limited preemption. SIAM J. Comput. 4, 478–490.Google Scholar
Gittins, J. C. (1979) Bandit processes and dynamic allocation indices (with discussion). J. R. Statist. Soc. B41, 148–177.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. et al. North-Holland, Amsterdam.Google Scholar
Glazebrook, K. D. (1976) Stochastic scheduling with order constraints. Int. J. Syst. Sci. 7, 657–666.CrossRefGoogle Scholar
Glazebrook, K. D. (1980) On stochastic scheduling with precedence relations and switching costs. J. Appl. Prob. 17, 1016–1024.Google Scholar
Glazebrook, K. D. (1981) On non-preemptive strategies in stochastic scheduling. Naval. Res. Logist. Quart. 28, 289–300.CrossRefGoogle Scholar
Glazebrook, K. D. (1982) On the evaluation of fixed permutations as strategies in stochastic scheduling. Stoch. Proc. Appl. 13, 171–187.Google Scholar
Glazebrook, K. D. (1982a) On the evaluation of suboptimal strategies for families of alternative bandit processes. J. Appl. Prob. 10, 716–722.Google Scholar
Glazebrook, K. D. (1983) Methods for the evaluation of permutations as strategies in stochastic scheduling. Management Sci. 29, 1142–1155.CrossRefGoogle Scholar
Glazebrook, K. D. (1985) Semi-Markov models for single-machine stochastic scheduling problems. Int. J. Syst. Sci. 16, 573–587.CrossRefGoogle Scholar
Glazebrook, K. D. (1987) Evaluating the effects of machine breakdowns in stochastic scheduling problems. Naval Res. Logist. Quart. 34, 319–335.Google Scholar
Meilijson, I. and Weiss, G. (1977) Multiple feedback at a single server station. Stoch. Proc. Appl. 8, 195–205.CrossRefGoogle Scholar
Nash, P. (1973) Optimal Allocation of Resources Between Research Projects. , Cambridge University.Google Scholar
Nash, P. (1980) A generalized bandit problem. J. R. Statist. Soc. B42, 165–169.Google Scholar
Ritchie, E. M. (1972) Planning and control of R and D activities. Operat. Res. Quart. 23, 477–490.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Whittle, P. (1980) Multi-armed bandits and the Gittins index. J. R. Statist. Soc. B42, 143–149.Google Scholar