Optimal aircraft load balancing

The Canadian Forces employ cargo aircraft for countless missions to deliver equipment, supplies and passengers. Maximizing the payload while maintaining a safe load balance is of high importance. This paper details a mathematical formulation, a Mixed Integer Linear Program model, to solve the problem of determining the arrangement of a set of items in a cargo hold that optimizes the load balance. Items are modelled as rectangles with specified dimensions, mass and centre of gravity offsets. The main decision variables determine the orientation and placement of a given set of items. The objective function can be chosen to minimize deviation of the centre of gravity from the target position or to maximize a function of the items loaded (cardinality, priority, etc.). The formulation models item rotation, spacing requirements, load ordering, macro items, obstacles and constrained placement. Furthermore, specialized cut and transitivity constraints are developed that limit the solution search space.