Minimizing the makespan in the two-machine no-wait flow-shop with limited machine availability

This paper deals with the two-machine no-wait flow-shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (Cmax). We prove that the problem is NP-Hard even if only one unavailability period occurs on one single machine, and NP-Hard in the strong sense for arbitrary numbers of unavailability periods. We also provide heuristic algorithms with error bounding analysis.