Given a weighted undirected graph G with a set of pairs of terminals (si, ti), i = 1 , … , d , and an integer L ≥ 2 , the two node‐disjoint hop‐constrained survivable network design problem is to find a minimum weight subgraph of G such that between every si and ti there exist at least two node‐disjoint paths of length at most L. This problem has applications in the design of survivable telecommunication networks with QoS‐constraints. We discuss this problem from a polyhedral point of view. We present several classes of valid inequalities along with necessary and/or sufficient conditions for these inequalities to be facet defining. We also discuss separation routines for these classes of inequalities, and propose a Branch‐and‐Cut algorithm for the problem when L = 3, as well as some computational results.
