With the current advances in aircraft design and Lithium-Ion batteries, electric aircraft are expected to serve as a replacement for conventional, short-range aircraft. This paper addresses the main operational challenges for short-range flights operated with electric aircraft: determining the investment needs for a fleet of electric aircraft, and the logistics of charging stations and swap batteries required to support these flights. A mixed-integer linear program with two phases is proposed. In the first phase, a schedule for flight and battery recharge is developed for a fleet of electric aircraft. In the second phase, optimal times for battery charging are determined, together with an optimal sizing of the number of charging stations and swap batteries. We illustrate our model for short-range flights to and from an European airport and for an electric aircraft designed based on the operational characteristics of a conventional, narrow-body aircraft.