Cyclic scheduling of operations for a part type in a flexible manufacturing system handled by a single robot: A parametric critical-path approach

We consider two problems of periodic scheduling of parts in a robotic production system functioning under a given repetitive robot's route. The objective is to determine the starting times and durations of processing operations so as to minimize the cycle length. We reduce the problems to finding parametric critical paths in networks with varying arc lengths. In contrast to previously known methods, which solve these cyclic scheduling problems in cubic time, the parametric network approach solves the problem in O(m² log m) time, m being the problem size.