A two-stage flow shop scheduling problem with transportation considerations

This paper considers a two-stage robotic flow shop scheduling problem of which the objective is to minimize the maximum completion time of all the jobs. The problem consists of two dedicated machines at the first stage and a single machine at the second stage. Each job is defined by two operations processed in series on two stages. Depending on the job type, each job is processed on a dedicated machine at the first stage, and is then transported, by a robot or a conveyor, to be processed on a single machine at the second stage. To tackle the problem, a mixed integer programming model is proposed, which is solved by CPLEX. This model is improved using valid inequalities based on three lower bounds. In addition, we establish the complexity of several variations of the problem and we identify special cases that can be solved in polynomial time. Furthermore due to the NP-hardness of the problem, two heuristics are proposed to solve approximately large-sized problems. The results indicate that the solutions obtained are of high quality and the corresponding CPU time is acceptable.