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A note on minimizing the expected makespan in flowshops subject to breakdowns

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  • Charles Du
  • Michael Pinedo

Abstract

Consider a two machine flow shop and n jobs. The processing time of job j on machine i is equal to the random variable Xij One of the two machines is subject to breakdown and repair. The objective is to find the schedule that minimizes the expected makespan. Two results are shown. First, ifP(X2j ≧ X1j) = 1 for all j and the random variables X11, X12,…, X1n are likelihood ratio ordered, then the SEPT sequence minimizes the expected makespan when machine 2 is subject to an arbitrary breakdown process; if P(X1j≧X2j) = 1 and X21, X22,….,X2n are likelihood ratio ordered, then the LEPT sequence minimizes the expected makespan when machine 1 is subject to an arbitrary breakdown process. A generalization is presented for flow shops with m machines. Second, consider the case where X1j and X2j are i.i.d. exponentially distributed with rate λj. The SEPT sequence minimizes the expected makespan when machine 2 is subject to an arbitrary breakdown process and the LEPT sequence is optimal when machine 1 is subject to an arbitrary breakdown process. © 1995 John Wiley & Sons, Inc.

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  • Charles Du & Michael Pinedo, 1995. "A note on minimizing the expected makespan in flowshops subject to breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1251-1262, December.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:8:p:1251-1262
    DOI: 10.1002/1520-6750(199512)42:83.0.CO;2-Q
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    References listed on IDEAS

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    1. Kevin D. Glazebrook, 1987. "Evaluating the effects of machine breakdowns in stochastic scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 319-335, June.
    2. Michael Pinedo, 1982. "Minimizing the Expected Makespan in Stochastic Flow Shops," Operations Research, INFORMS, vol. 30(1), pages 148-162, February.
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    Cited by:

    1. Jian Yang & Gang Yu, 2002. "On the Robust Single Machine Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 17-33, March.
    2. 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.

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