Variable neighborhood search for the location routing problem with multiple routes

We address a variant of the Location Routing Problem (LRP) where vehicles can perform several routes in the same planning period and both depots and vehicles have capacities. This problem represents a combination of two NP-hard problems: a vehicle routing problem, which determines the optimal set of routes to fulfill the demands of a set of customers, and a location problem, as the depots from which the vehicles performing the routes can be associated must be chosen from a set of possible locations. We propose a Variable Neighborhood Search (VNS) metaheuristic to solve this problem, and report on preliminary computational experiments conducted on a set of instances from the literature. To the best of our knowledge, this is the first time that a VNS based heuristic is proposed for solving this variant of the LRP.