The Robust Network Loading Problem under Polyhedral Demand Uncertainty: Formulation, Polyhedral Analysis and Computations * Ay¸ seg¨ ul Altın, Hande Yaman, and Mustafa C ¸ . Pınar Department of Industrial Engineering, Bilkent University, Ankara, Turkey {aysegula,hyaman,mustafap}@bilkent.edu.tr June 18, 2007 Abstract 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. Keywords: Network loading problem, polyhedral demand uncertainty, hose model, robust network design, polyhedral analysis, branch-and-cut. 1 Introduction Consider the following simple problem of deciding the optimal (i.e., resulting in the least total installation cost) number of devices of unit capacity to be installed on the links of the triangle- shaped network in Figure 1a to support the communication demands between the nodes. The number on each edge gives the capacity installation cost of a unit capacity device on that edge. The communication demands are forecasted to be one unit of traffic flow among all pairs of nodes in both directions. B C A (1) (0.5) (0.5) B C A 2 2 2 b) minimum cost design for deterministic demand a) initial network Figure 1: Example network for capacity loading * Research partially supported by TUBITAK-CNRS (TUBITAK project no. 105M322, CNRS project BOSPHORE No. 10843 TD). 1