Extensive facility location problems on networks: an updated review

Location problems with extensive facilities represent a challenging field of research. According to the specialized literature, a facility is called extensive if, for purposes of location, it is too large in relation to its environment to be considered a point. There are many examples of this type of structures that appear in real-world applications both in the continuous space (straight lines, circles, strips) and in networks (paths, cycles, trees). There exists a recent literature review on the location of dimensional facilities on continuous space (Díaz-Báñez et al. in TOP 154:22–44, 2004; Schöbel in Location of dimensional facilities in a continuous space, 2015) that does not cover similar problems on networks. The goal of this paper is to review the location of dimensional facilities in networks. We mainly concentrate on the location of paths and trees considering the most common objective functions in the location literature, namely median and center. However, we also consider some other alternative criteria generalizing them, as the ordered median objective function, or related to equity, reliability, and robustness. We include the basic tools and techniques that are applicable to develop algorithms for this kind of problems. Moreover, we present the best known complexity results for each of the considered problems. Finally, some suggestions are also made for possible directions of future research.