Stochastic proportionate flowshop scheduling with setups

This paper addresses the problem of scheduling n jobs on a proportionate tw o-machine flowshop where the machines are subject to random breakdowns and setup times are considered separate from processing times. The considered p erformance measure is makespan. Sequences that minimize makespan with proba bility 1 are obtained when the first or the second machine is subject to ra ndom breakdowns without making any assumptions about downtime distributions or counting processes. It is assumed that the processing and setup times o n one machine dominate the corresponding times on the other machine. In the case that processing and setup times on the first and second machines are proportionate, it is shown that the longest processing time (LPT) rule give s an optimal solution when only the first machine is subject to breakdowns, while the shortest processing time (SPT) rule yields an optimal solution w hen only the second machine suffers breakdowns. (C) 2001 Elsevier Science L td. hll rights reserved.