Upgrading nodes in tree-shaped hub location

TL;DR

This paper introduces a new optimization problem combining hub location, tree connectivity, and node upgrading, with improved formulations and computational results demonstrating enhanced solution quality.

Contribution

It formulates the Tree of Hubs Location Problem with Upgrading, integrating hub placement, tree structure, and node upgrading decisions, and develops strengthened MILP models.

Findings

Enhanced MILP formulations improve solution efficiency.

Valid inequalities significantly tighten the models.

Computational results show better solutions with strengthened formulations.

Abstract

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.