Evaluating the impact of uncertain trip duration and energy consumption on electric vehicle sharing network design

We consider an integrated electric vehicle sharing network (EVSN) design problem under uncertain trip duration and energy consumption. The aim of the problem is to jointly optimize the strategic decisions of the number of chargers to install in each sharing station and the number of electric vehicles (EVs) to purchase as well as the operational decisions of trip acceptance, vehicle relocation and recharging. The main objective is to maximize the profit of the EVSN operator while satisfying a given service level constraint. We propose a two-stage scenario-based stochastic programming approach, leading to a deterministic equivalent formulation of the problem as a mixed-integer linear program (MILP). Our numerical experiments on randomly generated instances allow us to evaluate the value of the stochastic solution (VSS), i.e. the benefit from using the stochastic model under uncertain trip duration and energy consumption instead of its deterministic counterpart. Our results highlight the higher performance of the stochastic model with regard to the feasibility and profitability of the obtained solution. They also show that the VSS depends on some features of the problem such as the size of the service region or the frequency of morning trips.