A Branch and Cut method for the Capacitated Location-Routing Problem

Most of the time in a distribution system, depot location and vehicle routing are interdependent and recent researches have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents two formulations of the location-routing problem with capacities on routes and depots and proposes an exact method based on a branch and cut approach using these formulations. The method is evaluated on two sets of randomly generated instances, and compared to heuristics and another lower bound