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 introduce an integer linear programming formulation based on the so-called cut formulation for the C-RSA problem. We describe several valid inequalities for the associated polytope, and further give necessary and sufficient conditions under which these inequalities are facet defining. Based on these results, we develop a branch-and-cut algorithm to solve the problem.