A variant of the permutation flow shop model with variable processing times

Abstract

We consider a modification of the classical flow shop problem with infinite buffer capacities. The processing times on various machines are variable: the more one delays the beginning of an operation, the longer is its processing time. There are many industrial applications for this model, for instance in the planning of machine maintenance or service and in steel production where the material will cool during the waiting periods and has to be reheated for the subsequent process. The problem turns out to be already NP-hard in the strong sense for two processors, and in general the optimal schedule is not a permutation schedule. In the literature, a restricted problem is considered where one wants to determine the optimal release times for the jobs, once their order is given. We shall solve this m-machine flow shop problem by a greedy placement algorithm. For the two-machine case, where also the optimal order of the jobs has to be determined, several approximate solution methods are analyzed.