Scheduling problems in a flowshop composed of two flexible machines

This paper studies the scheduling problems in a flowshop composed of two flexible machines, in which there are n identical jobs, each of which needs to be processed first on machine 1 with a processing time p1, then either processed separately on machine 1 with a processing time p12 or on machine 2 with a processing time p21, and finally processed on machine 2 with a processing time p2. Our purpose is to properly schedule the processing mode and the sequence in order to minimize the makespan. In this paper we give the analytic solution to this problem.