  In this paper, we introduce the Tree of Hubs Location Problem with Upgrading,
a mixture of the Tree of Hubs Location Problem, presented by Contreras et. al
(2010), and the Minimum Cost Spanning Tree Problem with Upgraded nodes, studied
for the first time by Krumke (1999). In addition to locate the hubs, to
determine the tree that connects the hubs and to allocate non-hub nodes to
hubs, a decision has to be made about which of the hubs will be upgraded,
taking into account that the total number of upgraded nodes is given. We
present two different Mixed Integer Linear Programming formulations for the
problem, tighten the formulations and generate several families of valid
inequalities for them. A computational study is presented showing the
improvements attained with the strengthening of the formulations and comparing
them.
