The Robust Network Loading Problem under Polyhedral Demand Uncertainty: Formulation, Polyhedral Analysis and Computations

We consider the Network Loading Problem under a polyhedral uncertainty description of traffic demands. After giving a compact multi-commodity formulation of the problem, we prove an unexpected decomposition property obtained from projecting out the flow variables, considerably simplifying the resulting polyhedral analysis and computations by doing away with metric inequalities, an attendant feature of most successful algorithms on the Network Loading Problem. Under a specific choice of the uncertainty description (hose model), we study the polyhedral aspects of Network Loading Problems, used as the basis of an efficient Branch-and-Cut algorithm supported by a simple heuristic for generating upper bounds. The results of extensive computational experiments on well-known network design instances are reported.