Multi-Objective Mixed-Integer Linear Optimisation of Aircraft Load Planning

Abstract: A general multi-objective optimisation model is developed for the load planning decision process of a bulk loaded commercial aircraft, using the Airbus A321 fitted with additional fuel tanks as a baseline platform. The model’s input is a specific set of load items, with associated quantities, mass and volume. The output is a load plan, stating where each item should be loaded and in what quantity. The load plans should be optimal with respect to a target centre of gravity range and handling efficiency. Furthermore, the solutions should be robust with respect to perturbations in the input data. Three objective functions and a set of constraints are defined to achieve this task. A constraint that ensures the ground stability of the aircraft is developed and analysed. A lexicographic approach is used solve the multi-objective problem, by sequentially solving a set of mixed-integer linear programs. The sequence is determined from a priority ranking of the objectives. Testing is carried out with data from an operator of the A321, with four different test cases. Test results indicate that the model is capable of solving the load planning problem for the baseline aircraft. The centre of gravity values are within the optimal range, and the load distributions are efficient. Additional margins on aircraft limits assist with maintaining feasibility in case of input perturbation. The model is also robust with respect to the highly variable test data. The main causes of infeasibility are mixing constraints and additional balance envelope margins. The ground stability constraint does not cause any significant amount of infeasibilities, and primarily increases the safety level of the load plans. A strength of the model is its relatively simple handling of the multiple objectives, and the small number of tunable parameters also makes the model controllable. A trained agent in the industry is able to understand and control the model without an extensive technical background. The test process used differs slightly from the actual industry load planning process. As a result, testing only allows for evaluation of the model’s ability to solve the load planning problem, and gives no justification for implementation in real-world operations. Such an evaluation requires a prototype to be tested in an operational environment using the actual process. As testing was only done for the baseline aircraft, with one set of test data and model parameters, a justifiable conclusion cannot be reached on the model’s applicability to other bulk loaded aircraft. Therefore, it is recommended to carry out further testing on different aircraft as the next step in them model’s evaluation. iv