Exact solution of hub network design problems with profits

This paper considers hub network design problems with profits in which the simultaneous optimization of the collected profit, setup cost of the hub network and transportation cost are considered. An exact algorithmic framework is proposed for two variants of this class of problems, where a sophisticated Lagrangean function that exploits the structure of the problems is used to efficiently obtain bounds at the nodes of an enumeration tree. In addition, reduction tests and partial enumerations are used to considerably reduce the size of the problems and thus help decrease the computational effort. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed algorithmic framework.