A survey of recent research on location-routing problems

The design of distribution systems raises hard combinatorial optimization problems. For instance, facility location problems must be solved at the strategic decision level to place factories and warehouses, while vehicle routes must be built at the tactical or operational levels to supply customers. In fact, location and routing decisions are interdependent and studies have shown that the overall system cost may be excessive if they are tackled separately. The location-routing problem (LRP) integrates the two kinds of decisions. Given a set of potential depots with opening costs, a fleet of identical vehicles and a set of customers with known demands, the classical LRP consists in opening a subset of depots, assigning customers to them and determining vehicle routes, to minimize a total cost including the cost of open depots, the fixed costs of vehicles used, and the total cost of the routes. Since the last comprehensive survey on the LRP, published by Nagy and Salhi (2007), the number of articles devoted to this problem has grown quickly, calling a review of new research works. This paper analyzes the recent literature (72 articles) on the standard LRP and new extensions such as several distribution echelons, multiple objectives or uncertain data. Results of state-of-the-art metaheuristics are also compared on standard sets of instances for the classical LRP, the two-echelon LRP and the truck and trailer problem.