Minimizing the number of robots to meet a given cyclic schedule

We study a problem of cyclic no-wait scheduling of identical parts on m sequential machines. A number of robots are used to transport the parts from one machine to another. We consider the problem that has two performance measures: one is the number of robots to be used, the other is the period of a cyclic schedule. We find the minimal number of robots needed to meet a given cyclic schedule, for all possible cycle lengths, the complex-ity of the suggested algorithm being O(m 5 ), independently of the range within which the cycle length value may vary.