Fleet size problem for one-way electric carsharing services considering customers’ waiting tolerance and waiting stress

Service operation problems arising from electric carsharing services have been the research subject of many scholars in the past few years. Previous studies did not consider customers’ psychological waiting stress in the decision-making of electric carsharing services. This study addresses a fleet size problem for one-way electric carsharing services while considering vehicle relocation, vehicle charging, and customers’ waiting tolerance as well as psychological waiting stress. A mixed-integer nonlinear programming (MINLP) model is first developed for the problem. By exploring the model convexity, we put forward an effective outer-approximation algorithm such that the ε-optimal solution can be obtained. Numerical experiments are conducted to demonstrate the efficacy of the proposed model and solution method. We also analyze how the consideration of customers’ waiting tolerance and waiting stress influences the fleet size, system profitability, and service level.