Designing Private Line Networks

We study a capacitated network design problem arising in the design of private line networks. Given a complete graph, a subset of its node set (the "hub" set), and point-to-point traffic demands, the objective is to install capacity on the edges (using several batch sizes and nonlinear costs), and route traffic in the resulting capacitated network, so that 1) all the demand between a pair of nodes is routed along a single path, and 2) the demand is either sent directly from source to sink, or via a number of hub nodes. We first formulate an initial integer program, and various approximations to it. Valid inequalities are then derived for a special knapsack problem involving both integer and 0-1 variables arising from the capacity constraints on an edge. These and related inequalities are then used to strengthen the formulations. Computational results using these inequalities within a general purpose branch-and-cut system are presented