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Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time

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  • Ali Allahverdi
  • John Mittenthal

Abstract

The problem of scheduling n jobs on m parallel machines is considered when the machines are subject to random breakdowns and job processing times are random variables. An objective function of mean flow time is developed for a general parallel machine system, and an expression of its expected value is derived. The problem is transformed into a deterministic unrelated parallel machine scheduling model with modified processing times when the number of breakdowns is modeled as a generalized Poisson process. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Ali Allahverdi & John Mittenthal, 1994. "Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(5), pages 677-682, August.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:5:p:677-682
    DOI: 10.1002/1520-6750(199408)41:53.0.CO;2-7
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    References listed on IDEAS

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    1. W. A. Horn, 1973. "Technical Note—Minimizing Average Flow Time with Parallel Machines," Operations Research, INFORMS, vol. 21(3), pages 846-847, June.
    2. Emmons, Hamilton & Pinedo, Michael, 1990. "Scheduling stochastic jobs with due dates on parallel machines," European Journal of Operational Research, Elsevier, vol. 47(1), pages 49-55, July.
    3. J. Birge & J. B. G. Frenk & J. Mittenthal & A. H. G. Rinnooy Kan, 1990. "Single‐machine scheduling subject to stochastic breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 661-677, October.
    4. John Mittenthal & M. Raghavachari, 1993. "Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties," Operations Research, INFORMS, vol. 41(4), pages 786-796, August.
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    Cited by:

    1. Allahverdi, Ali, 1999. "Stochastically minimizing total flowtime in flowshops with no waiting space," European Journal of Operational Research, Elsevier, vol. 113(1), pages 101-112, February.
    2. Xiaoqiang Cai & Sean Zhou, 1999. "Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs," Operations Research, INFORMS, vol. 47(3), pages 422-437, June.

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