High hopes are put in electric vehicles to lower global green house gas emissions. From an operational perspective, however, their limited range and the long recharging times add considerable complexity to the decision tasks planning their efficient application. In this context, we treat a problem setting where a single electric vehicle executes transport requests along a straight line, which, for instance, occurs when cranes, automated guided vehicles, or shuttles handle boxes in container terminals. From time to time the vehicle needs to be recharged and, thus, has to visit some charging station also located on the line. We investigate the scheduling of a single electric vehicle, so that the makespan for executing all transport requests is minimized and the vehicle is timely recharged. The solution algorithm developed is then applied to also explore the location planning of charging stations.