The Fleet Assignment Problem (FAP) deals with assigning aircraft types to the scheduled flights based on fleet capabilities, aircraft availabilities, flight requirements, and operational costs. Due to high operating costs, the large number of flights scheduled each day, and the dependency of the following processes in the airline scheduling processes on FAP output, solving the FAP has always been a challenging task for the airlines. In this work, a revised integer linear programming model is proposed for solving the daily FAP. The model has an objective function of minimizing the operating cost of assigning a fleet type to a specific flight. In addition, the proposed model of the daily FAP aims to satisfy the following constraints: flight cover, aircraft type balance, fleet size, flight traffic (demand), flight flying altitude, and runway length requirements. The proposed model was successfully applied on a real-world dataset related to a national airline and solved using Gurobi software. Furthermore, sensitivity analysis has been performed to show the effect of changing different FAP parameters on the obtained results.