This paper deals with the Electric Vehicle Scheduling and Optimal Charging Problem.More precisely, given a fleet of Electric Vehicles - EVs and Combustion Engine Vehicles - CVs, aset of tours to be processed by vehicles and a charging infrastructure, the problem aims to optimizethe assignment of vehicles to tours and minimize the charging cost of EVs, while considering severaloperational constraints mainly related to chargers, electricity grid, and EVs driving range. We provethat the Electric Vehicle Scheduling and Charging Problem (EVSCP) is NP-hard in the ordinary sense.We provide a mixed-integer linear programming formulation to model the EVSCP and use CPLEX tosolve small and medium instances. To solve large instances, we propose two heuristics: a SequentialHeuristic - SH and a Global Heuristic - GH. The SH considers the EVs sequentially. To each EV, itassigns a set of tours and guarantees the feasibility of a charging schedule using the Maximum WeightClique Problem. Then, it generates an optimal charging schedule for this EV using a Minimum CostFlow formulation. However, the GH computes, in the first step, a feasible assignment of tours to allEVs. In the second step, it applies a global Min-Cost-Flow-based charging algorithm to minimize thecharging cost of the EVs fleet. To evaluate the efficiency of our solving approaches, computationalresults on a large set of real and randomly generated test instances are reported and compared. Testedinstances include large random instances with up to 200 EVs and 320 tours.