Stochastic survivable network design problems: Theory and practice

Abstract

We study survivable network design problems with edge-connectivity requirements under a two-stage stochastic model with recourse and finitely many scenarios. For the formulation in the natural space of edge variables we show that facet defining inequalities of the underlying polytope can be derived from the deterministic counterparts. Moreover, by using graph orientation properties we introduce stronger cut-based formulations. For solving the proposed mixed integer programing models, we suggest a two-stage branch&cut algorithm based on a decomposed model. In order to accelerate the computations, we suggest a new technique for strengthening the decomposed L-shaped optimality cuts which is computationally fast and easy to implement. A computational study shows the benefit of the decomposition and the cut strengthening – which significantly reduces the number of master iterations and the computational running time. Moreover, we evaluate the stability of the scenario generation method and analyze the value of the stochastic solution.