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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 …