Location of Connection Facilities

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Inspired by real-world applications, the connection location-allocation problem is an exciting and multi-faceted problem in location theory. Modeling the transportation of goods, we are given flows between existing facilities. Each flow must pass a connection facility which may, e.g., represent a transshipment terminal or a processing facility. In order to minimize the total transportation costs, we are interested in finding favorable locations of these connection facilities and low-priced allocations of the flows. This location problem represents the central subject matter of this work which is composed of three parts: theoretical analysis, solution methods, and model extensions. In order to derive very general results, we principally consider location problems in the multi-dimensional space with abstract cost functions. The theoretical analysis and the development of solution methods is based on a general class of multi-facility location problems. For this reason, the results can be transferred to a wide variety of related biconvex optimization problems ranging from applications in cluster analysis to image registration.