A bi-level programming approach to locate capacitated electric vehicle charging stations

We consider the design of a charging infrastructure based on fast-charging capacitated stations to enable electric vehicles to carry out long-distance trips. We focus on taking into account the impact of the non-system-optimal drivers' behavior on the station capacity consumption in the modeling of the facility location problem. This leads to the formulation of a bi-level optimization model. In this bi-level program, the upper level represents the station location problem faced by the charging infrastructure provider and the lower level represents the selfish behavior of EV drivers who will seek to use the charging stations opened by the infrastructure provider to carry out their trips with a minimum number of stops. We propose a solution approach based on the reformulation of the bi-level program into a mixed-integer linear program thanks to the use of the primal-dual optimality conditions of linear programming. Our preliminary computational experiments carried out on small instances show the impact on the global system performance of ignoring the selfish drivers' behavior and the potential benefit from using a bi-level programming model.