Single-allocation Hub Network Design Decision with Upgrading.

Resumen

We will talk about di↵erent formulations for the uncapacitated single allocation hub location problem with upgraded connections and incomplete hub networks. Upgrading connections aims to reduce the transportation costs between sites that are connected by the upgraded edges. Two types of connections are considered to be upgraded: interhubs edges and edges that connect origin/destination points to hubs. Single-allocation hub location models can be classified into two families: path-based formulations and flow based formulations. We propose different formulations inspired by the former ones to model the upgrading version of this problem considering complete and incomplete networks. Observe that in this problem, the decision variables are the locations of hubs, the allocations of the nodes to the hubs, the connections used between hubs, and the edges to be upgraded. The network obtained must be connected since any site can send flow to any other site. Moreover, the number of inter-hub edges as well as the number of connections between origin/destination points and hubs to be upgraded, are established as parameters. For the resulting formulations, valid inequalities and an ad-hoc preprocessing phase is developed to strengthen them. We report on a series of computational tests performed to assess the models proposed and their enhancements.