ISBN 978-3-8439-4734-3

978-3-8439-4734-3, Reihe Mathematik

Thomas Ullmert
Hub Location: Finite Dominating Sets and Interdiction Problems

121 Seiten, Dissertation Technische Universität Kaiserslautern (2021), Hardcover, A5

Zusammenfassung / Abstract

Hub location has become one of the major streams of location science during the last three decades. Hub location is about installing hubs that serve as distribution centers and setting up an inter-hub network with reduced transportation costs. A wide variety of models for hub location problems have been developed over the years. The rapid growth in this area can be explained by its practical applicability and the interesting theoretical background which is the combination of location problems and network design problems. Over the years, many solution methods, ranging from exact methods to heuristic procedures have been proposed.

In this thesis, two variants of hub location problems, namely planar hub median location problems and discrete hub median location interdiction problems, are considered. Planar hub median location problems seek for optimal locations of hubs in the plane, which lead to an infinite number of possible candidates. In this work, a special distance measure, a so-called polyhedral gauge is considered. Although the set of candidate solutions for planar hub median location problems with polyhedral gauges is infinite, in this work, the consideration of a finite number of candidate solutions is proven to be sufficient to obtain an optimal solution.

Discrete hub median location interdiction problems are two-player games. The first player, called the locator, seeks for an optimal choice of hubs, which performs best in case of a threat. However, the threat is caused by the second player, called the interdictor. The interdictor reduces the performance of the hub choice as much as possible. Both players are assumed to have full knowledge of each other's behavior. Two variants of the discrete hub median location interdiction problem are considered and formulated as bi-level programs. By using tools of integer programming, the formulations are improved and interesting insights on the structure of their solutions are obtained.