The electric location-routing problem: Formulation and Benders decomposition approach

In this paper, we focus on a problem that requires location of recharging stations and routing of electric vehicles in a goods distribution system. The goods are disseminated from a depot and distributed to the customers via electric vehicles with limited capacity. Differently from the classical vehicle routing problem, the vehicles have battery restrictions that need to be recharged at some stations if a trip is longer than their range. The problem reduces to finding the optimal location of the recharging stations and their number to minimize the total cost, which includes the routing cost, the recharging cost, and the fixed costs of opening stations and operating vehicles. We propose a novel mathematical formulation and an efficient Benders decomposition algorithm to solve this environmental logistics problem. Our methods solve the problem in a general setting with non-identical stations and vehicles by allowing multiple visits to the stations and partial recharging.