With recent developments in the airline industry worldwide, the competition among the industry has increased largely with many key players in the market. In order to generate profits, the industry has paid much attention to generate optimal routes that are maintenance feasible. The main aim of operational aircraft maintenance routing problem (OAMRP) is to generate these optimal routes for each aircraft that are maintenance feasible and follow the constraints defined by the Federal Aviation Administration (FAA). In this paper, the OAMRP is studied with two main objectives. First, to propose a formulation of a network flow-based Integer Linear Programming (ILP) framework for the OAMRP that considers three main maintenance constraints simultaneously: maximum flying-hour, limit on the number of take-offs between two consecutive maintenance checks and the work-force capacity. Second, to develop a new reinforcement learning-based algorithm which can be used to solve the problem, quickly and efficiently, as compared to commonly available optimization software. Finally, the evaluation of the proposed algorithm on real case datasets obtained from a major airline located in the Middle East verifies that the algorithm generates high-quality solutions quickly for both medium and large-scale flight schedule dataset.