The Meaning of Permutation in Reentrant Permutation Flow Shop Problems

In a flow shop, jobs are serially processed on a set of machines, and the machine order is the same for all the jobs. In a permutation flow shop, there is an additional assumption that the order in which jobs enter the machines is the same on each machine. While the meaning of "permutation" is clear for a flow shop, it is more ambiguous for a reentrant flow shop. In a reentrant flow shop, jobs are processed on some machines more than once. Then, there are several ways to understand the meaning of permutation. We indicate that different researchers use the term "permutation" for different assumptions. Our effort is to clear up this ambiguity. This is significant for definition clarity when studying the reentrant scenario. Moreover, the various definitions influence proposed heuristics for solving the problem and, by that, also influence the quality of the resulting solutions. We show this through basic examples as a first step towards more extensive experiments.