A computational evaluation of constructive heuristics for the parallel blocking flow shop problem with sequence-dependent setup times

This paper deals with the problem of scheduling jobs in a parallel flow shop environment without buffers between machines and with sequence-dependent setup times in order to minimize the maximum completion time of jobs. The blocking constraint normally leads to an increase in the maximum completion time of jobs due to the blockage of machines, which can increase even more so when setup times are considerable. Hence, the heuristic to solve this problem must take into account these specificities in order to minimize the timeout of machines. Because the procedures designed to solve the parallel flow shop scheduling problem must deal not only with the sequencing of jobs but also with their allocation to the flow shops, 36 heuristics have been tested in this paper, of which 35 combine sequencing rules with allocation methods while the last one takes a different approach that is more related to the nature of this problem. The computational evaluation of the implemented heuristics showed good performance of the heuristic designed especially for the problem (RCP0) when the setup times are considerable. Furthermore, the evaluation has also allowed us to propose a combined heuristic that leads to good solutions in a short CPU time.