Minimizing the cycle time of multiple-product processing networks with a fixed operation sequence, setups, and time-window constraints

We solve a special case of the single-robot cyclic scheduling problem with a fixed robot operation sequence and time window constraints on processing times. It generalizes the known single-part fixed-sequence problems into the one to cover a processing network with multiple part types and setup time requirements between the processing steps for different parts at the shared stations. The objective is to minimize the cycle time. We prove that this problem is equivalent to the parametric critical path problem, and propose a strongly polynomial time solution algorithm which uses a new labeling procedure to identify all feasible parameter values. The proposed algorithm is based on an extension to the known Bellman-Ford algorithm. The occurrence of time windows together with multiple products and a network-type process makes our problem much more complex than that of the single-product single processing-line case. One key observation from this study is that in spite of this generalization, the problem is proved to be solvable by the proposed parametric critical path algorithm. Its complexity, though not as good as that for the single-product problem, still remains strongly polynomial and, as such, dominates the complexity of general linear programming methods in this case. This observation makes our result a candidate optimization subroutine to be used in heuristic algorithms that solve general cyclic scheduling problems with time windows and setup time constraints and that allow different robot operation sequences in a cycle to be evaluated.