Optimizing Aircraft Weight and Balance for Two‐Leg Flight Operations

Unnecessary unloading and reloading operations of unit loading devices (ULDs) at intermediate airports increase operational costs and turnaround times in air cargo transportation involving two flight legs. Existing studies on the aircraft weight and balance problem (WBP) for multi‐leg flights have not fully addressed these extra operations. While focusing on ULD path‐blocking, they neglected critical operational factors such as sequence swaps, hold exchanges, and position shifts between flight legs. To address this research gap, we develop a precise mixed‐integer linear programming (MILP) model for WBP with two legs (WBP‐2L) through analysis of scenarios and causes of the extra operations. The model aims to maximize total payload while minimizing center of gravity (CG) deviations, extra operations, and ULD position shifts, subject to practical constraints including stowage position requirements, aircraft CG envelope specifications, and flight leg connectivity rules. To enhance computational efficiency, we propose a novel logic‐based Benders decomposition (BD) algorithm that strategically decomposes the problem into a position‐allocation master problem and a CG‐check subproblem. Furthermore, an innovative ULD position‐shifting strategy is introduced to strengthen the solution. Experimental results demonstrate that adopting the ULD position‐shifting strategy not only reduces extra operations but also improves the CG. Compared to sequential single‐leg optimization, the WBP‐2L model achieves a significant 78.3% reduction in ULD operations. Additionally, in comparison with state‐of‐the‐art studies, the WBP‐2L model yields the fewest extra operations. These results indicate that the proposed method is both practical and scalable for real‐world applications.