With the rapid development of the civil aviation industry, airlines face many challenges in managing fleet operations. Among these, the engine replacement strategy has a significant impact on flight reliability and operational costs. Through an in-depth analysis of the civil aviation engine replacement business scenario, a mixed-integer programming model was constructed with the goal of minimizing engine fleet operation costs. The model considers factors such as engine cascading operations and leasing. The strategies of engine installation, removal, and repair were studied, and a generalized variable neighborhood search algorithm was designed to solve the model. Numerical experiments and sensitivity analyses were conducted using China Southern Airlines as an example, with different scales. The results of the numerical experiments show that the algorithm's solution quality outperforme both the variable neighborhood search algorithm and the Gurobi solver. Finally, the sensitivity analysis provided management insights for engine fleet operations.