A case study of a two-stage flow shop with dedicated machines and a single robot

This paper considers a two-stage robotic flow shop scheduling problem. The objective is to minimize the makespan. The problem consists of two dedicated machines at the first stage and one common machine at the second stage. Each job is defined by two operations processed on the two-stages in series. Depending on its type, each job is executed on a dedicated machine at the first stage, then it is transported, by a robot or a conveyor, to be executed on the common machine at the second stage. We propose two mixed-integer program (MIP) models to solve this problem which is NP-Hard. These two models can be improved using valid inequalities based on three lower bounds. In addition, due to the NP-hardness of this case, a heuristic is developed to solve approximately large-size problems. The results indicate that the obtained solutions are of high quality and the corresponding CPU time is acceptable.