Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-27T00:29:07.095Z Has data issue: false hasContentIssue false
  • English
  • Français

A General Model for the Scheduling of Alternative Stochastic Jobs that may Fail

Published online by Cambridge University Press:  27 July 2009

N. A. Fay  and
K. D. Glazebrook
N. A. Fay
Affiliation:
Department of Statistics University of Newcastle upon Tyne United Kingdom
K. D. Glazebrook
Affiliation:
Department of Statistics University of Newcastle upon Tyne United Kingdom
Get access Rights & Permissions [Opens in a new window]

Extract

The standard single-machine scheduling problem is modified to take into account unsuccessful job completions. We use a result due to Nash to analyze problems in which some jobs are alternative to one another in the sense that only one of a set of alternative jobs need be completed successfully. Conditions are proposed under which a nonpreemptive strategy is optimal for processing such a system.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 2 , April 1989 , pp. 199 - 221
Copyright
Copyright © Cambridge University Press 1989

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

REFERENCES

Bergman, S. W. & Gittins, J. C. (1986). Statistical methods for pharmaceutical research planning. New York: Marcel Dekker.Google Scholar
Bruno, J. & Hofri, M. (1975). On scheduling chains of jobs on one processor with limited preemption. SIAM Journal of Computing 4: 478–490.CrossRefGoogle Scholar
Deshmukh, S.D. & Chikte, S.D. (1977). Dynamic investment strategies for a risky R&D project. Journal of Applied Probability 14: 144–152.CrossRefGoogle Scholar
Gittins, J.C. (1979). Bandit processes and dynamic allocation indices (with discussion). Journal of the Royal Statistical Society B41: 148–177.Google Scholar
Gittins, J.C. & Jones, D.M. (1974). A dynamic allocation index for the sequential design of experiments. In Gani, & Vincze, (eds.), Progress in statistics. Amsterdam: North Holland.Google Scholar
Glazebrook, K.D. (1980). On stochastic scheduling with precedence relations and switching costs. Journal of Applied Probability 17: 1016–1024.CrossRefGoogle Scholar
Glazebrook, K.D. (1982). On the evaluation of fixed permutations as strategies in stochastic scheduling. Stochastic Processes and their Applications 13: 171–187.CrossRefGoogle Scholar
Glazebrook, K.D. (1982). On the evaluation of suboptimal strategies for families of alternative bandit processes. Journal of Applied Probability 10: 716–722.CrossRefGoogle Scholar
Glazebrook, K.D. (1983). Methods for the evaluation of permutations as strategies in stochastic scheduling. Management Science 29; 1142–1155.CrossRefGoogle Scholar
Glazebrook, K.D. (1987). Evaluating the effects of machine breakdowns in stochastic scheduling problems. Naval Research Logistics Quarterly 34: 314–335.Google Scholar
Glazebrook, K.D. & Fay, N.A. (1987). On the scheduling of alternative stochastic jobs on a single machine. Advances in Applied Probability 19: 955–973.CrossRefGoogle Scholar
Glazebrook, K.D. & Fay, N.A. (1987). Evaluating strategies for generalized bandit problems. International Journal of Systems Science 19: 1605–1613.CrossRefGoogle Scholar
Nash, P. (1973). Optimal allocation of resources between research projects. Ph.D. Thesis, Cambridge University, England.Google Scholar
Nash, P. (1980). A generalized bandit problem. Journal of the Royal Statistical Society B 42: 165–169.Google Scholar
Ritchie, E.M. (1972). Planning and control of R&D activities. Operations Research Quarterlies 23: 477–490.CrossRefGoogle Scholar
Ross, S.M. (1970). Applied probability models with optimization applications. San Francisco, California: Holden-Day.Google Scholar
Weber, R.R. (1979). Optimal organization of multiserver systems. Ph.D. Thesis, Cambridge University, England.Google Scholar
Whittle, P. (1980). Multiarmed bandits and the Gittins index. Journal of the Royal Statistical Society B 42: 143–149.Google Scholar