Determining the optimal number of duplicated process tanks in a single-hoist circuit board production line

In a circuit board production line, each circuit board carrier must be soaked in a sequence of process tanks and the soak time at each process tank must be within a prespecified time interval. Processes with long minimum soak times can create severe bottlenecks. It is common practice to add duplicates of the tanks for these processes to improve the throughput of the line. This paper studies the problem of determining the optimal number of duplicated process tanks to be used in each process that maximizes the throughput for a given tank configuration of a single-hoist circuit board production line. The problem is formulated as a mixed integer program. The properties of the optimal solution are derived. On the basis of these properties, an algorithm is developed to solve the problem optimally. Computational experience with the benchmark problems is discussed.