A robust optimization approach to multi-interval location-inventory and recharging planning for electric vehicles

This paper introduces a multi-interval battery swapping station location-inventory and recharging planning problem for electric vehicles (BSS-LIRP). The research problem jointly determines battery swapping station location, battery inventory level and recharging plan at each located station with the minimal total system cost, including station construction cost, battery inventory cost and recharging cost over multiple time intervals. We firstly formulate the deterministic problem by an integer programming model. Next two robust models are established by considering data uncertainty: when flow demand is uncertain, we adopt the budget of uncertainty robustness approach to control the conservativeness; when electricity prices are uncertain, we apply the robust optimization approach with multiple ranges to deal with the uncertainty in each time interval. The experimental results show the applicability of the deterministic model. We find that in the presence of large variation of flow demand and electricity prices, it is beneficial for stations to strategically delay recharging some batteries. Furthermore, the solutions to the robust model reveal the significant impacts of the uncertainty in flow demand and electricity prices on the electric vehicle infrastructure network design and operations strategies.