The rising demand for electric vehicles (EVs), motivated by their environmental benefits, is generating an increased need for EV charging infrastructure. Also, it has been recognized that the adequacy of such infrastructure helps promote EV use. Therefore, to facilitate EV adoption, governments seek guidance on continued investments in EV charging infrastructure development. Such investment decisions, which include EV charging station locations and capacities, and the timing of such investments require robust estimates of future travel demand and EV battery range constraints. This paper develops and implements a framework to establish an optimal schedule and locations for new charging stations and decommissioning gasoline refueling stations over a long-term planning horizon, considering the uncertainty in future travel demand forecasts and the driving range heterogeneity of EVs. A robust mathematical model is proposed to solve the problem by minimizing not only the worst-case total system travel cost but also the total penalty for unused capacities of charging stations. This study uses an adaptation of the cutting-plane method to solve the proposed model. Based on two key decision criteria (travelers' cost and charging supply sufficiency), the results indicate that the robust scheme outperforms its deterministic counterpart.