A Polynomial Algorithm for No-Wait Cyclic Multi-Hoist Scheduling

This paper addresses cyclic scheduling of multiple hoists in a no-wait electroplating line with constant processing times. The objective is to minimize the cycle time, or equivalently maximizing the production throughput, for a given number of hoists. The problem is first formulated as a set of prohibited intervals for the cycle time. We then prove that the optimal cycle time is necessarily one of special values of the cycle time, and thus reduce the problem to a feasibility-checking problem for a given value of the cycle time. We show that the latter problem can be transformed to a longest path problem in a directed graph. The complete algorithm is shown to be polynomial in the number of tanks in an electroplating line