Multi-family scheduling in a two-machine reentrant flow shop with setups

This paper considers a two-machine multi-family scheduling problem with reentrant production flows. The problem consists of two machines, M1 and M2, and each job has the processing route (M1, M2, M1, M2). There are identical jobs in the same family and the jobs in the same family are processed in succession. Each machine needs a setup time before the first job in a family is processed. The objective is to minimize the maximum completion time. Examples of such a problem occur in the bridge construction, semiconductor industry and job processing on numerical controlled machines, where they usually require that the jobs are reprocessed once and there are identical jobs in the same family. This problem is shown to be NP-hard. A branch-and-bound algorithm is proposed, and computational experiments are provided.