Single-machine scheduling with periodic and flexible periodic maintenance to minimize maximum tardiness

This paper considers a single-machine scheduling problem with several maintenances periods. Specifically, two situations are investigated. In the first one, maintenance periods are periodically fixed: maintenance is required after a periodic time interval. In the second one, the maintenance is not fixed but the maximum continuous working time of the machine which is allowed is determined. The objective is to minimize the maximum tardiness. These problems are known to be strongly NP-hard. We propose some dominance properties and an efficient heuristic. Branch-and-bound algorithms, in which the heuristics, the lower bounds and the dominance properties are incorporated, are proposed and tested computationally.