Electric Vehicle Routing under Time-Variant Electricity Prices

The integration of electric vehicles (EVs) with the energy grid has become an important area of research due to the increasing EV penetration in today's transportation systems. Under appropriate management of EV charging and discharging, the grid can currently satisfy the energy requirements of a considerable number of EVs. Furthermore, EVs can help enhance the reliability and stability of the energy grid through ancillary services such as energy storage. This paper proposes the EV routing problem with time windows under time-variant electricity prices (EVRPTW-TP) which optimizes the routing of a fleet of electric vehicles that are delivering products to customers, jointly with the scheduling of the charging and discharging of the vehicles from/to the grid. The proposed model is a multiperiod vehicle routing problem where electric vehicles can stop at charging stations to either recharge their batteries or inject stored energy to the grid. Given the energy costs that vary based on time-of-use, the charging and discharging schedules of the EVs are optimized to benefit from the capability of storing energy by shifting the demand from peak hours to off-peak hours when the price of energy is lower. The vehicles can recover the cost of energy and potentially realize profits by injecting energy back to the grid at high price periods. EVRPTW-TP is formulated as an optimization problem and a Lagrangian relaxation approach as well as a hybrid variable neighborhood search/tabu search heuristic are proposed to obtain high quality solutions. Numerical experiments on instances from the literature are provided. The proposed model is also evaluated on the case study of a grocery delivery service at the region of Kitchener-Waterloo in Ontario, Canada. Insights on the impacts of energy pricing, service time slots, as well as fleet size are presented.