Electric vehicle routing problem with time-dependent waiting times at recharging stations

In the Electric Vehicle Routing Problem with Time Windows (EVRPTW) the vehicles have a limited driving range and must recharge their battery at some points on their route. The recharging stations have a limited capacity and the newly arriving vehicles may have to queue before being recharged. In this study, we model the EVRPTW considering time-dependent queueing times at the stations. We allow but penalize late arrivals at customer locations and at the depot. We minimize the cost of vehicles, drivers, energy, and penalties for late arrivals. We formulate the problem as a mixed integer linear program and solve small instances with CPLEX. For the larger instances, we develop a matheuristic which is a combination of Adaptive Large Neighborhood Search and of the solution of a mixed integer linear program. We perform an extensive experimental study to investigate the impact of queueing at the recharging stations on the routing decisions. The results show that waiting at the stations may increase the total cost by 1%–26%, depending on the problem type and queue length. We also observe that recharges tend to shift to less crowded mid-day hours due to the time-dependent waiting times.