Multiple allocation hub-and-spoke network design under hub congestion

The multiple allocation hub-and-spoke network design under hub congestion problem is addressed in this paper. A non-linear mixed integer programming formulation is proposed, modeling the congestion as a convex cost function. A generalized Benders decomposition algorithm has been deployed and has successfully solved standard data set instances up to 81 nodes. The proposed algorithm has also outperformed a commercial leading edge non-linear integer programming package. The main contribution of this work is to establish a compromise between the transportation cost savings induced by the economies of scale exploitation and the costs associated with the congestion effects.