Adopting electric vehicles is essential to reducing greenhouse gas emissions and achieving climate goals. However, the existing electrical grid can easily be overloaded with more electric vehicles on the road. For this reason, many researchers are working on developing relevant charging infrastructures that include charging scheduling strategies. These strategies aim to control charging power efficiently and economically. This paper addresses the electric vehicle charging scheduling problem at a public charging station with a limited number of chargers and a limited overall power capacity. Before arriving at the charging station, electric vehicle drivers submit their charging demands. Then, the scheduler reserves a suitable charger for each vehicle and allocates the right amount of power so that the final state-of-charge at the departure time is as close as possible to the requested one. We present two variants of the problem, a constant output power model and a variable power model. We show that these charging scheduling problems are strongly NP-hard, and we propose heuristics and simulated annealing combined with linear programming to solve them. Simulation results show the efficiency of the proposed approaches for maximizing the state-of-charge of electric vehicles.