High profitability and high costs have stiffened competition in the airline industry. The main purpose of the study is to propose a computationally efficient algorithm for integrated fleet assignments and aircraft routing problems for a real-case hub and spoke airline planning problem. The economic concerns of airline operations have led to the need for minimising costs and increasing the ability to meet rising demands. Since fleets are the most limited and valuable assets of airline carriers, the allocation of aircraft to scheduled flights directly affects profitability/market share. The airline fleet assignment problem (AFAP) addresses the assignment of aircraft, each with a different capacity, capability, availability, and requirement, to a given flight schedule. This study proposes a mathematical model and heuristic method for solving a real-life airline fleet assignment and aircraft routing problem. We generate a set of problem instances based on real data and conduct a computational experiment to assess the performance of the proposed algorithm. The numerical study and experimental results indicate that the heuristic algorithm provides optimal solutions for the integrated fleet assignment and aircraft routing problem. Furthermore, a computational study reveals that compared with the heuristic method, solving the mathematical model takes significantly longer to execute.