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A Note on Stochastic Shop Models in Which Jobs have the Same Processing Requirements on Each Machine

Author

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  • Michael Pinedo

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We consider stochastic models for flow shops, job shops and open shops in which the work required by job j is the same at each machine, being a random variable W j . Because machines operate at different speeds, S i , the processing time of job j at machine i is W j /S i ,. It is the main result of this note that in a flow shop where the machine speeds increase (decrease) from the first to last machine and the workload distributions are ordered by a likelihood ratio criterion, then the makespan of the jobs is stochastically minimized by processing the jobs in the order of least to greatest (greatest to least) workload.

Suggested Citation

  • Michael Pinedo, 1985. "A Note on Stochastic Shop Models in Which Jobs have the Same Processing Requirements on Each Machine," Management Science, INFORMS, vol. 31(7), pages 840-846, July.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:7:p:840-846
    DOI: 10.1287/mnsc.31.7.840
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    Cited by:

    1. Yu, Tae-Sun & Pinedo, Michael, 2020. "Flow shops with reentry: Reversibility properties and makespan optimal schedules," European Journal of Operational Research, Elsevier, vol. 282(2), pages 478-490.
    2. S.S. Panwalkar & Milton L. Smith & Christos Koulamas, 2013. "Review of the ordered and proportionate flow shop scheduling research," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 46-55, February.

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