Exact approaches for routing capacitated electric vehicles

Abstract

We investigate a variant of the standard Capacitated Vehicle Routing Problem (CVRP), where each vehicle is powered exclusively by electricity stored in its rechargeable battery. Consequently, each vehicle should visit not only customer nodes but also (possibly) some charging stations before the battery got depleted. The importance of this problem stems from the fact that logistics companies are increasingly relying on electric vehicles in urban distribution. We propose three exact approaches. The first one requires solving a compact polynomial-sized formulation. The second approach is a branch-and-cut algorithm. An original feature of this algorithm is that it embeds the first exact separation of the well-known rounded capacity constraints. Finally, the third approach is a hybrid algorithm that requires solving an augmented variant of the compact formulation. We report the results of a computational study that was carried out on a set of 125 instances, providing evidence that the polynomial-sized formulation can consistently solve instances having up to 30 customer nodes and 21 charging stations, and that the hybrid algorithm solves some instances having up to 100 customer nodes and 21 charging stations while requiring moderate CPU times. Furthermore, the proposed approach was shown to exhibit limitations in solving some large-scale tightly-constrained instances.