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

Charles Du and Michael Pinedo

Naval Research Logistics (NRL), 1995, vol. 42, issue 8, 1251-1262

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.

Date: 1995
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