Chance Constrained Network Design

the thesis deals with important problem of planning of telecommunication networks (and other networks which carry demand between different network nodes requiring allocation of capacities along the network links). More specifically, the problem is to find the network with the minimal cost which will satisfy uncertain demand. Two descriptions of uncertainty are considered. In the first one the demand matrices belong to a known set defined by different sets of linear constraints, this approach of robust optimization. In the second one the demand matrices belong to a given set with some specified probability, this problem formulation can be classified as stochastic programming problem with probability (chance) constraints. - In robust setting an interesting and important special case is found when the static routing in certain sense gives no worse results as dynamic routing. - In chance constrained case several approximate deterministic formulations are developed and studied. These approximations are critical from the point of view of computability because the original chance constrained formulation presents considerable computational difficulties. Extensive numerical experiments with different problem formulations are presented which allows to analyze meaningfully relative properties of different approximations