A hierarchical algorithm for the planar single‐facility location routing problem

Location routing problem (LRP) is an important logistical problem that comprises two of the main logistical drivers namely facility location and vehicle routing. In this paper, we focus on the planar single‐facility LRP with Euclidean distance where the location of the facility can be anywhere in the space and not restricted to a given set of potential sites only as in the discrete case. A hierarchical heuristic‐based method is put forward which continuously takes into account the information from the routing results while systematically improving the location using the end‐points of the obtained routes. In addition, some enhancement schemes that include a set of local searches as well as diversification and intensification mechanisms are also incorporated into the search. The proposed method outperformed the existing approaches when tested on the data sets taken from the literature. Our approach produced nine new best results out of the fifteen in the literature besides being relatively robust when compared to the existing methods.