Using clustering analysis in a capacitated location-routing problem

The location routing problem (LRP) appears as a combination of two difficult problems: the facility location problem (FLP) and the vehicle routing problem (VRP). In this work, we consider a discrete LRP with two levels: a set of potential capacitated distribution centres (DC) and a set of ordered customers. In our problem we intend to determine the set of installed DCs as well as the distribution routes (starting and ending at the DC). The problem is also constrained with capacities on the vehicles. Moreover, there is a homogeneous fleet of vehicles, carrying a single product and each customer is visited just once. As an objective we intend to minimize the routing and location costs.Several authors have integrated cluster analysis procedures in heuristics for LRPs. As a contribution to this direction, in this work several hierarchical and non-hierarchical clustering techniques (with several proximity functions) are integrated in a sequential heuristic algorithm for the above mentioned LRP model. All the versions obtained using different grouping procedures were tested on a large number of instances (adapted from data in the literature) and the results were compared so as to obtain some guidelines concerning the choice of a suitable clustering technique.