Electric vehicle routing with charging/discharging 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 an EV fleet that are delivering products to customers, jointly with the scheduling of the charging and discharging of the EVs from/to the grid. The proposed model is a multiperiod vehicle routing problem where EVs 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 energy demands from peak hours to off-peak hours when the energy price is lower. The vehicles can recover the energy costs and potentially realize profits by injecting energy back to the grid at high price periods. EVRPTW-TP is formulated as an optimization problem. A Lagrangian relaxation approach and a hybrid variable neighborhood search/tabu search heuristic are proposed to obtain high quality lower bounds and feasible solutions, respectively. Numerical experiments on instances from the literature are provided. The proposed heuristic is also evaluated on a case study of an EV fleet providing grocery delivery at the region of Kitchener-Waterloo in Ontario, Canada. Insights on the impacts of energy pricing, service time slots, range reduction in winter as well as fleet size are presented.