Integrally indecomposable polytopes and the survivable network design problem

We consider the survivable network design problem for fractional flows and integral capacities and demands. While this problem was modelled using so-called metric inequalities in the past, we will present an integer program which is based on the automatic linearization of non-linear constraints. It turns out that the linear relaxation of the latter formulation is actually stronger than the linear relaxations of the previously known models. Our model making use of integrally indecomposable polytopes, we introduce a new way of computing these polytopes via the chamber decomposition of the parameter space.