Abstract
This paper deals with the makespan minimizations problem in an n-item, three-stage flowshop production system. Each stage is assigned to a machine, and a processed job for a product is composed of four elementary operations. The machine assignments for the three elementary operations are fixed, but that for the remaining elementary operation is free. Thus a schedule is determined according to the machine assignment to an elementary operation and the operations sequencing in each machine. The study clarified that the operation sequencing is easily determined under a limited processing time constraint and showed the sufficient condition for obtaining the optimal schedule through theoretical analysis. Another research result is a proposal of optimal solution algorithm based on the branch and bound method, together with a numerical example and concrete procedure. The study also discussed the scheduling problem where the free assignment of machine to an elementary operation is limited to machine no. 1 and machine no. 3.
