This study focuses on the optimization of green ammonia production systems through a mixed-integer linear programming (MILP) framework. The proposed model integrates both design decisions and detailed annual operational strategies, evaluated at an hourly resolution. Due to the model's complexity and large-scale nature, solving it directly using commercial optimization software is computationally prohibitive. To overcome this challenge, we employ a generalized Benders decomposition method with “no-good” cuts, significantly improving the efficiency of the solution process. Our approach is demonstrated on a real-world case study in Inner Mongolia, China. The resulting design plan and operational strategy achieve a payback period of 8.8 years. Furthermore, computational experiments with different commercial solvers confirm that the proposed algorithm outperforms direct resolution in most cases.