## Large-scale hierarchical networks: How to compute an optimal architecture?

Please always quote using this URN: urn:nbn:de:0297-zib-7799
• In this article, we present a mathematical model and an algorithm to support one of the central strategic planning decisions of network operators: How to organize a large number of locations into a hierarchical network? We propose a solution approach that is based on mixed-integer programming and Lagrangian relaxation techniques. As major advantage, our approach provides not only solutions but also worst-case quality guarantees. Real-world scenarios with more than 750 locations have been solved within 30 minutes to less than 1\% off optimality.

$Rev: 13581$