When considering hub-and-spoke networks with single allocation, the absence of alternative routes makes this kind of systems specially vulnerable to congestion effects. In order to improve the design of such networks, congestion costs must be addressed. This article deploys two different techniques for addressing congestion on single allocation hub-and-spoke networks: the Generalized Benders Decomposition and the Outer Approximation method. Both methods are able to solve large scale instances. Computational experiments show how the adoption of advanced solution strategies, such as Pareto-optimal cut generation on the Master Problem branch-and-bound tree, may be decisive. They also demonstrate that the solution effort is not only associated with the size of the instances, but also with their combination of the installation and congestion costs.

O problema de projeto de redes arborescentes de fonte única com custos convexos é abordado neste trabalho. Trata-se de problema referencial no projeto de redes de transporte de matéria, energia ou informação. Resulta do esforço de modelagem um programa não-linear inteiro misto de grande escala e de difícil resolução. Para superar tais dificuldades, dois métodos distintos são aplicados ao problema: O primeiro deles é a técnica de Decomposição de Benders Generalizada; o segundo método combina a técnica de Aproximação Externa com as idéias de projeção subjacentes à Decomposição de Benders para derivar a técnica OA-Híbrido. O método OA-Híbrido se mostra muito eficiente na solução de instâncias com até 702 arcos, obtendo custos de computação bastante razoáveis, tornando promissora a sua aplicação a problemas ainda mais sofisticados.

In this work, the single source tree network design problem under convex costs is addressed. This is a referential problem when designing networks for materials, energy or data transportation. The modeling effort yields a large scale mixed-integer nonlinear program which is very hard to solve. In order to overcome the solution difficulties, two distinct solution methods are deployed: The first of them is the Generalized Benders Decomposition method; the second technique combines the Outer Approximation method with the ideas of projection in Benders Decomposition in order to imply the technique Hybrid-OA. The Hybrid-OA method is very effective on solving instances up to 702 edges, under reasonable computational costs, and makes the further application of the proposed technique to even more sophisticated models promising.

In this work, a mixed integer nonlinear programming model combining direct service links, demand uncertainty and congestion effects is proposed. This model is efficiently solved by Generalized Benders Decomposition, for instances of moderate sizes and reasonable number of scenarios. The deployed algorithms are further used for re-designing the Brazilian air transportation network, enabling the analysis of future demand scenarios and providing decision support about the optimal investment policy for Brazil.