Variable disaggregation in network flow problems with piecewise linear costs

We study mixed-integer programming formulations, based upon variable disaggregation, for generic multicommodity network flow problems with nonconvex piecewise linear costs, a problem class that arises frequently in many application domains in telecommunications, transportation, and logistics. We present several structural results for these formulations, and we analyze the results of extensive experiments on a large set of instances with various characteristics. In particular, we show that the linear programming relaxation of an extended disaggregated model approximates the objective function by its lower convex envelope in the space of commodity flows. Together, the theoretical and computational results allow us to suggest which formulation might be the most appropriate, depending on the characteristics of the problem instances.