Optimal Scheduling of Two-Stage Reentrant Hybrid Flow Shop for Heat Treatment Process

Abstract

The reentrant hybrid flow shop for a heat treatment process is considered in this study. We consider job scheduling in a reentrant hybrid flow shop problem that consists of two statges in series. The first stage is washing, followed by heat treating in the second stage. Each job passes through the first and second stages, respectively, and then re-enter the first stage one more time. Since the first stage must process the jobs twice (with different processing times depending upon the type of the jobs), it becomes the bottleneck in this flow shop problem. To resolve this problem, the jobs needed to be better sequenced to balance the load among the first and the second stages. The objective is to minimize makespan of a set of jobs and increase the utilization of the both stages. This problem was formulated as a mixed integer program (MIP). The results from the data set show that the utilization of the second stage (heat treating) increased from 79.5% to their full capacity at 100%, exceeding the target set by the company at 95%.