The ROADEF 2020 challenge presents a maintenance scheduling problem from the Frenchelectricity grid company RTE. The modeling of uncertainty makes the problem highly nonconvexand apparently out of the reach of mathematical solvers. We present our approach for the challengeproblem. It is based on a new family of cutting planes, coupled with a constraint generationapproach. We present mathematical proofs and separation algorithms for the cutting planes. Wethen study the practical impact of our additions on the challenge instances, showing that ourapproach significantly reduces the optimality gap obtained by the solv