Optimal Upgrading Schemes For Effective Shortest Paths In Networks

In this paper, a generalization of a recently proposed optimal path problem concerning decisions for improving connectivity is considered [see 6]. Each node in the given network is associated with a connection delay which can be reduced by implementing upgrading actions. For each upgrading action a cost must be paid, and the sum must satisfy a budget constraint. Given a fixed budget, the goal is to choose a set of upgrading actions such that the total delay of establishing paths among predefined node pairs is minimized. This model has applications in areas like multicast communication planning and wildlife reserve design.A novel formulation is provided along with an ad-hoc branch-and-cut and a stabilized Benders decomposition algorithm. These strategies exploit connections of the considered problem with other well-known network design problems. Computational results on a large set of instances show the efficacy of the proposed preprocessing methods and optimization algorithms with respect to existing alternatives for the problem. Complementary, the scalability of the models and the corresponding algorithms is investigated with the aim of answering questions raised by [6].