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Consider a flexible flow shop with s stages in series and at each stage a number of identical machines in parallel. There are n jobs to be processed and each job has to go through the stages following the same route. Job j has release date rj, due date dj, weight wj and a processing time pjl at stage l, l=1,…,s. The objective is to minimize the total weighted tardiness of the n jobs. In this paper we describe and analyse three heuristics. The first one is a decomposition algorithm that solves the problem by decomposing the flexible flow shop problem into a series of single-stage scheduling subproblems. The second one is an algorithm based on local search. The third heuristic is a hybrid algorithm that combines the first two. We conclude with a comparative study of the three heuristics. Copyright © 2000 John Wiley & Sons, Ltd.

We study the special case of the m machine flow shop problem in which the processing time of each operation of job j is equal to pj; this variant of the flow shop problem is known as the proportionate flow shop problem. We show that for any number of machines and for any regular performance criterion we can restrict our search for an optimal schedule to permutation schedules. Moreover, we show that the problem of minimizing total weighted completion time is solvable in O(n²) time. © 1998 John Wiley & Sons, Ltd.

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