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We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation for a predefined set of admissible logical links that takes many practical side constraints into account, including node hardware, several bit-rates, and survivability against single physical node or link failures. This model is solved using a branch-and-cut approach with cutting planes based on either of the two layers. On several realistic two-layer planning scenarios, we show that these cutting planes are still useful in the multi-layer context, helping to increase the dual bound and to reduce the optimality gaps.