The hub-and-spoke network design problem, also known as the hub location problem, aims to find the concentration points in a given network flow so that the sum of the distances of the linkages is minimized. In this work,we compare discrete solutions of this problem, given by the branch-and-cutmethod applied to the p-hubmedianmodel, with continuous solutions, given by the hyperbolic smoothing technique applied to a min-sum-min model. Computational experiments for particular instances of the Brazilian air transportation system, with the number of hubs varying from 2 to 8, are conducted with the support of a discretization heuristic and the Voronoi diagram. © 2013 Brazilian Operations Research Society.