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论文类型：期刊论文

发表时间：2010-03-01

发表刊物：INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS

收录刊物：SCIE、EI、Scopus

卷号：124

期号：1

页面范围：151-158

ISSN号：0925-5273

关键字：Scheduling; Two parallel machine; Makespan; Total completion time; Multiple maintenance; Bin-packing problem

摘要：This paper deals with the problem of processing a set of n jobs on two identical parallel machines. In order to reduce the probability of machine breakdown with minor sacrifices in production time, the machines cannot process the jobs consecutively, they need to be maintained regularly (here we assume that the largest consecutive working time for each machine cannot exceed an upper limit T). Two scheduling models are considered. In the first model, the maintenance activities are performed periodically and the objective is to schedule the jobs on two machines such that the makespan is minimized. In the second model, the maintenance activities are determined jointly with the scheduling of jobs, and the objective is to minimize the total completion time of jobs. For the first problem we, introduce an O(n(2)) time algorithm named MH(FFD) and show that the performance ratio of MH(FFD) is at most max{1.6+1.2 sigma,2}, where sigma((Delta) under bar)t/T, t is the amount of time to perform each maintenance activity. For the second problem, we apply the classical SIT algorithm to it and show that the worst-case bound of SPT algorithm is no more than 1 + 2 sigma. We also point out that for the case of single machine, if the SPT schedule has three batches, then the upper bound of SPT algorithm can be reduced from the known result 21/17 to 11/9 under the assumption that t < T. (C) 2009 Elsevier B.V. All rights reserved.