The topic of this Master thesis is an in-depth research study on a specific type of network systems known as hub-and-spoke networks. In particular, we study q-Hub Arc Location Problems that consist, at a strategical level, of selecting q hub arcs and at most p hub nodes, and of the routing of commodities through the so called hub level network. We propose strong formulations to two variants of the problem, namely the q-hub arc location problem and the q-hub arc location problem with isolated hub nodes.
We present a Lagrangian relaxation that exploits the structure of these problems by decomposing them into |K|+2 independent easy-to-solve subproblems and develop Lagrangian heuristics that yield high quality feasible solutions to both models. We, further, provide some insights on the structure of the optimal solutions to both models and investigate the cost benefit of incomplete hub networks with and without isolated hub nodes. Finally, computational results on a set of benchmark instances with up to 100 nodes are reported to assess the performance of the proposed MIP formulations and of our algorithmic approach
