Single Facility Location on Networks

Abstract

This chapter discusses the problem of selecting one point of a network to optimize one or several functions that are distance-dependent with respect to given points of the network. The problem is motivated by a number of potential applications. For example, a plant is set up at some point of a transportation system to minimize production and shipment costs; an emergency service unit is located in a rural area to minimize the maximal intervention time to population centers; and a switching center is located in a communication network to minimize transmission costs from and toward peripheral units. Network location theory is traced back to obtained a characterization of the median set of a tree. However, this was only a side-result of a study devoted to automorphisms of quadratic forms. The chapter presents the main models, theorems, and algorithms for the location of a single facility on a network. The chapter focuses on results recently found and approaches that have emerged during the past five years. This includes various extensions of the median and center problems, as well as the location of a facility by voting and competitive processes.