A Two-Stage Decomposition-Grouping Strategy for Multi-Aircraft Weight and Balance Optimization of Non-ULD

This study investigates the weight balance problem in loading non-unit load devices (non-ULDs) for multi-aircraft. A two-stage weight balance optimization model was developed for multi-aircraft non-ULDs loading. The first stage involves a two-dimensional geometric constraint model for distributing non-ULDs positions, considering their constraints, with multi-objectives of maximizing aircraft cargo hold area utilization and payload, and minimizing aircraft sorties. The second stage is a weight and balance model for adjusting non-ULDs positions, considering various aircraft constraints. Two solution strategies are designed: first, decomposing the two-stage model into a two-dimensional geometric constraint model and a weight balance constraint model via logical checks; second, a grouping strategy that combines non-ULDs in pairs to form blocks. Using Gurobi, two scenarios with different combined solution strategies were verified for the B747F aircraft. The results indicate that, for large scale instances with a given number of non-ULD, the Gurobi decomposition with grouping delivers the best balance of solution quality and solving speed. On average, cargo hold utilization is 58.59%, the number of aircraft sorties is 11.25, and solver time is 108.19 s. Directly solving with Gurobi performs worse, with cargo hold utilization of 45.04%, the number of aircraft sorties is 13.75, and solver time of 1,689.29 s. The results from the Gurobi grouping strategy are very close to those from the Gurobi decomposition with grouping strategy, with averages of 58.59% cargo hold utilization, the number of aircraft sorties is 11.25, and 76.62 s for solver time. In contrast, the Gurobi decomposition strategy yields averages of 44.95% cargo hold utilization, the number of aircraft sorties is 13.75, and 957.28 s of solver time. All methods delivered an average payload of 1,154,489 kg for 11.25 to 13.75 sorties. The proposed model can realize the loading of batch non-ULDs across multi-aircraft. Relative to the decomposition strategy, the designed grouping strategy substantially accelerates solving time while maintaining competitive solution quality.