Cyclic scheduling in a robotic production line

The solution of cyclic scheduling problems is part of the classical repertoire on scheduling algorithms. We consider a problem of cyclic scheduling of identical parts in a production line where transportation of the parts between machines is performed by several robots. The problem is to find co-ordinated movements of the parts and robots in the line with the no-wait constraints imported; the objective is to maximize the throughput rate. Unlike many previous algorithms which are either heuristic or at best solve the single-robot version of the problem in O(m⁴ log m) time, the proposed algorithm provides an exact solution for the more complicated case of multiple robots and solves the problem in O(m³ log m) time, where m denotes the number of machines in the line.