This paper considers a single machine scheduling problem with several maintenances periods. Specically, two situations are investigated. In the rst one, maintenance periods are periodically xed: maintenance is required after a periodic time interval. In the second one, the maintenance is not xed 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 ecient heuristic. Branch-and-bound algorithms, in which the heuristics, the lower bounds and the dominance properties are incorporated, are proposed and tested computationally.

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A management of multi-stacks fuel cell systems is proposed to extend systems useful life in a Prognostics and Health Management (PHM) framework. The problem consists in selecting at each time which fuel cell stacks have to run and which output power has to be chosen for each of them to satisfy a load demand as long as possible. Multi-stacks fuel cell system useful life depends not only on each stack useful life, but also on both the schedule and the operating conditions settings that define the contribution of each stack over time. As the impact of variable operating conditions on fuel cell lifetime is not well-known, a simplified representation of fuel cell behavior under wear and tear is used to estimate the available outputs over time and their associated Remaining Useful Lives (RUL). This health state prognostics model is configured to suit to Proton-Exchange Membrane Fuel Cells (PEMFC) specific characteristics. The proposed scheduling process makes use of an optimal approach based on a Mixed Integer Linear Program (MILP). Efficiency of the associated commitment strategy is assessed by comparison with basic intuitive strategies, considering constant and piecewise constant load demand profiles.