The constrained-routing and spectrum assignment (C-RSA) problem is a key issue when dimensioning and designing an optical network. Given an optical network G and a multiset of traffic demand K, it aims at determining for each traffic demand k ∈ K a path and an interval of contiguous slots while satisfying technological constraints and optimizing some linear objective function(s). In this paper, we first introduce an integer linear programming formulation for the C-RSA problem. We further investigate the facial structure of the associated polytope.