Analysis of proportional machine allocation scheme in a deterministic reentrant line

This paper analyzes the properties of a proportional machine allocation scheme in a reentrant production line of one product and one machine group. The scheme allocates machines to each production stage proportional to the workload of the stage. It is proved that given initial work-in-process (WIP) distribution and a constant work release rate in the capacity of the line, there exists a unique, full machine capacity allocation for the line; when the proportional machine allocation scheme is repetitively applied over time, the whole reentrant line is eventually balanced. These results obtained under such a simplified scenario also provide some insights to the dynamics and resource allocation problem of a reentrant line.