Transit authorities are rapidly replacing conventional buses with electric ones because of the increasing concerns about air quality, greenhouse gas emissions, and energy demand. Many mathematical optimization models have been developed for scheduling conventional buses. However, such models would not fit electric buses (EBs) due to their limited travelling range and long charging time. Moreover, such operational differences have prompted new research into the literature on the charging station location problem for EBs. This study combines EB scheduling with fast-charging infrastructure location planning with the objective of minimizing the total costs of scheduling, including deadhead trips, electricity and ownership costs of EBs, as well as the cost of establishing fast-chargers. We propose a Mixed-Integer Linear Programming (MILP) formulation for an arc-based model and an Integer Linear Programming (ILP) formulation for a path-based model and solve them with Cplex solver and branch-and-price algorithm, respectively. The two solution approaches have been tested for various instances with different numbers of trips and potential charging locations. The computational experiments show that the branch-and-price algorithm is more computationally efficient in terms of execution time compared to the arc-based model solved with Cplex. Finally, a sensitivity analysis was conducted to identify the most cost-effective EB type, considering the real characteristics of different EB types. Moreover, we assessed how changes in battery capacity and the maximum travel range of EBs impact the optimal solution.