Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T15:46:17.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic scheduling on a repairable machine with Erlang uptime distribution

Part of: Operations research and management science Special processes Survival analysis and censored data

Published online by Cambridge University Press:  01 July 2016

Wei Li ,
W. John Braun  and
Yiqiang Q. Zhao
Wei Li*
Affiliation:
University of Winnipeg and Chinese Academy of Sciences
W. John Braun*
Affiliation:
University of Winnipeg
Yiqiang Q. Zhao*
Affiliation:
University of Winnipeg
*
∗ Postal address: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, China.
∗ Postal address: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, China.
∗ Postal address: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, China.
Get access Rights & Permissions [Opens in a new window]

Abstract

A set of jobs is to be processed on a machine which is subject to breakdown and repair. When the processing of a job is interrupted by a machine breakdown, the processing later resumes at the point at which the breakdown occurred. We assume that the machine uptime is Erlang distributed and that processing and repair times follow general distributions. Simple permutation policies on both machine parameters and the processing distributions are given which minimize the weighted number of tardy jobs, weighted flow times and the weighted sum of the job delays.

Keywords

Stochastic schedulingbreakdownsErlang uptimesnon-preemptive resume model

MSC classification

Primary: 90B35: Scheduling theory, deterministic
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 62N05: Reliability and life testing
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998 , pp. 1073 - 1088
Copyright
Copyright © Applied Probability Trust 1998 

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

Adiri, I., Bruno, J., Frostig, E. and Rinnooy Kan, A. H. G. (1989). Single machine flow-time scheduling with a single breakdown. Acta Informat. 26, 679–696.CrossRefGoogle Scholar
Allahverdi, A. (1995). Two-stage production scheduling with separated setup times and stochastic breakdowns. J. Operat. Res. Soc. 46, 896–904.CrossRefGoogle Scholar
Allahverdi, A. and Mittenthal, J. (1994). Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time. Naval Res. Logist. 41, 677–682.Google Scholar
Allahverdi, A. and Mittenthal, J. (1994). Two-machine ordered flowshop scheduling under random breakdowns. Math. Comp. Modeling 20, 9–17.Google Scholar
Allahverdi, A. and Mittenthal, J. (1995). Scheduling on a two-machine flowshop subject to random breakdowns with a makespan objective function. Eur. J. Operat. Res. 81, 376–387.Google Scholar
Birge, J., Frenk, J. B. G., Mittenthal, J. and Rinnooy Kan, A. H. G. (1990). Single machine scheduling subject to stochastic breakdowns. Naval Res. Logist. 37, 660–677.3.0.CO;2-3>CrossRefGoogle Scholar
Chang, C. S., Chao, X. L., Pinedo, M. and Weber, R. (1992). On the optimality of LEPT and Cμ rules for machines in parallel. J. Appl. Prob. 29, 667–681.Google Scholar
Chaudhry, M. L. and Templetion, J. G. C. (1983). A First Course in Bulk Queues. Wiley, New York.Google Scholar
Cox, D. R. (1955). The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proc. Camb. Phil. Soc. 51, 433–441.Google Scholar
Du, Q. and Pinedo, M. (1995). A note on minimizing the expected makespan in flowshops subject to breakdowns. Naval Res. Logist. 42, 1251–1262.3.0.CO;2-Q>CrossRefGoogle Scholar
Frenk, J. B. G. (1987). Renewal theory and completely monotone functions. Report No. 8759/A, Econometric Institute, Erasmus University, Rotterdam.Google Scholar
Frenk, J. B. G. (1991). A general framework for stochastic one-machine scheduling problems with zero release times and no partial ordering. Prob. Eng. Inf. Sci. 5, 297–315.CrossRefGoogle Scholar
Frostig, E. (1991). A note on stochastic scheduling on a single machine subject to breakdown – the preemptive repeat model. Prob. Eng. Inf. Sci. 5, 349–354.Google Scholar
Glazebrook, K. D. (1984). Scheduling stochastic jobs on a single machine subject to breakdowns. Naval Res. Logist. Quart. 31, 251–264.Google Scholar
Glazebrook, K. D. (1987). Evaluating the effects of machine breakdowns in stochastic scheduling problems. Naval Res. Logist. Quart. 34, 319–335.3.0.CO;2-5>CrossRefGoogle Scholar
Glazebrook, K. D. (1991). On non-preemptive policies for stochastic single machine scheduling with breakdown. Prob. Eng. Inf. Sci. 5, 77–87.CrossRefGoogle Scholar
Li, W. and Cao, J. H. (1994). Stochastic scheduling on an unreliable machine with general uptimes and general setup times. J. Syst. Eng. Syst. Sci. 3, 279–288.Google Scholar
Li, W. and Cao, J. H. (1995). Stochastic scheduling on a single machine subject to multiple breakdowns according to different probabilities. Operat. Res. Lett. 18, 81–92.Google Scholar
Li, W. and Glazebrook, K. D. (1998). On stochastic machine scheduling with general distributional assumptions. Eur. J. Operat. Res. 105, 525–536.Google Scholar
Mittenthal, I. (1986). Scheduling on single machine subject to breakdowns. . University of Michigan, Ann Arbor, MI.Google Scholar
Pinedo, M. (1983). Stochastic scheduling with release dates and due dates. Operat. Res. 31, 559–572.Google Scholar
Pinedo, M. (1995). Scheduling: Theory, Algorithms, and Systems. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Pinedo, M. and Rammouz, E. (1988). A note on stochastic scheduling on a single machines subject to breakdown and repair. Prob. Eng. Inf. Sci. 2, 41–49.Google Scholar
Righter, R. (1994). Scheduling. In Stochastic Orders and Their Applications, ed. Shaked, M. and Shanthikumar, J. G., Academic Press, New York, pp. 381–432.Google Scholar
Righter, R. and Shanthikumar, J. G. (1989). Scheduling multiclass single server queueing systems to stochastically maximise the number of successful departures. Prob. Eng. Inf. Sci. 3, 323–333.Google Scholar
Ross, S. M. (1983). Introduction to Stochastic Dynamic Programming. Academic Press, New York.Google Scholar