A Metaheuristic for the Periodic Location-Routing Problem

The well-known Vehicle Routing Problem (VRP) has been generalized toward tactical or strategic decision levels of companies but not both. The tactical extension or Periodic VRP (PVRP) plans trips over a multi-period horizon, subject to frequency constraints. The strategic extension or Location-Routing Problem (LRP) tackles location and routing decisions simultaneously as in most distribution systems interdependence between these decisions leads to low-quality solutions if depots are located first, regardless the future routes. Our goal is to combine for the first time the PVRP and LRP into the Periodic LRP or PLRP. A metaheuristic is proposed to solve large size instances of the PLRP. It is based on our Randomized Extended Clarke and Wright Algorithm (RECWA) for the LRP and it tries to take into consideration several decision levels when making a choice during the construction of a solution. The method is evaluated on three sets of instances and results are promising. Solutions are compared to the literature on particular cases such as one-day horizon (LRP) or one available depot (PVRP).