Bilinear programming formulations for Weber problems with continuous and network distances

While travel cost in urban areas is generally best modeled using network distances, continuous distance measures are mostly used for location problems in rural environments. Combining both is not only interesting from a modeling perspective, but has also computational advantages since it combines reduced storage requirements for the network data with a high accuracy of the approximated distances. In this paper, Weber problems with combined distance measures are discussed. If continuous distances are measured using block norm distances, the resulting Weber problems can be represented by bilinear programming formulations. Theoretical properties of this model are discussed, and two possible solution strategies are suggested.