Decomposition Methods for Network Optimization Problems in the Presence of Uncertainty

We develop a new algorithmic approach for solving network design problems in the presence of uncertainty. These problems can be formulated as stochastic programming problems with recourse. We propose two algorithms which combine successive polyhedral approximation of the objective function and related decomposition techniques with stochastic quasigradient methods. Numerical experiments suggest considerable speed up of convergence compared with more traditional techniques. These methods are applied to the problem of design of high speed data network based on Asynchronous Transfer Mode in the case of uncertainty about demand evolution.