Minimizing the number of robots to meet a given cyclic schedule

The authors 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. They 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. The authors find the minimal number of robots needed to meet a given cyclic schedule, for all possible cyclic lengths, the complexity of the suggested algorithm being O(m⁵), independently of the range within which the cycle length value may vary.