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We study the maintenance task scheduling problem for an aircraft fleet in an uncertain environment from the viewpoint of robust optimization. Given a daily horizon, the maintenance tasks delegated to a shop should be scheduled in such a way that sufficient aircrafts are available on time to meet the demand of planned missions. The tasks are either scheduled maintenance activities or unexpected repair jobs when a major fault is detected during pre-or after-flight check of each mission. The availability of skilled labour in the shop is the main constraint. We propose a robust formulation so that the maintenance tasks duration is subject to unstructured uncertainty due to the environmental and human factors. As a result of the specific structure of the primary model and non-convexity of the feasible space, the classical robust optimization methods cannot be applied. Thus, we propose an ϵ-Conservative model in tandem with Monte-Carlo sampling to extract the set of all feasible solutions corresponding to various disturbance vectors. Since the one-way sampling-thenoptimization approach does not guarantee the probabilistic feasibility, we employ a hybrid simulationoptimization approach to ensure that the solutions provided by the ϵ-Conservative model are robust to all uncertainty scenarios. The experimental results confirm the scalability of the proposed methodology by generating the robust optimal solutions, satisfying all conservatism levels and uncertainty scenarios irrespective of the problem size.