The Electric Two-echelon Vehicle Routing Problem

Two-echelon distribution systems are attractive from an economical standpoint and help keeping large vehicles out of densely populated city centers. Large trucks can be used to deliver goods to intermediate facilities in accessible locations, whereas smaller vehicles allow to reach the final customers. Due to their reduced size, pollution, and noise emissions, multiple distribution companies around the world have adopted an electric fleet for last-mile deliveries. Route planning in multi-tier logistics leads to notoriously difficult problems. This difficulty is accrued in the presence of an electric fleet, since each vehicle must operate on a smaller range, and may require planned visits to charging stations. To study these challenges, we introduce the electric two-echelon vehicle routing problem (E2EVRP) as a prototypical problem. We propose a large neighborhood search metaheuristic as well as an exact mathematical programming algorithm, which uses decomposition techniques to 1 ar X iv :1 80 3. 03 62 8v 1 [ cs .D S] 9 M ar 2 01 8 enumerate promising first-level solutions, in conjunction with bounding functions and route enumeration for the second-level routes. These sophisticated algorithms produce optimal or near-optimal solutions for the problem, and allow us to carefully evaluate the impact of several defining features of optimized battery-powered city distribution networks. In particular, through a simple simulation of a metropolitan area via representative of E2EVRPs benchmark instances, we observe that the detour miles due to recharging decrease proportionally to 1/ρx with x ≈ 5/4 as a function of the charging stations density ρ ; e.g., in a scenario where the density of charging stations is doubled, recharging detours are reduced by 58%. The range of the electric vehicles has an even bigger impact, as in our experiments, an increase of battery capacity to a range of 150km helps performing the majority of suburban delivery tours without need for en-route recharging.