Formulations for the nonbifurcated hop-constrained multicommodity capacitated fixed-charge network design problem

This paper addresses the multicommodity capacitated fixed-charge network design problem with nonbifurcated flows and hop constraints. We present and compare mathematical programming formulations for this problem and we study different relaxations: linear programming relaxations, Lagrangean relaxations and partial relaxations of the integrality constraints. In particular, for the hop-indexed formulation, we show that the Lagrangean bound obtained by relaxing the flow conservation equations is tighter than the linear programming relaxation bound. We present computational results on a large set of randomly generated instances. Acknowledgements.