Optimal Aircraft Load Balancing – Mathematical Formulation


  1. Kaluzny, B.L.
  2. Shaw, R.H.A.D.
Corporate Authors
Defence R&D Canada - Centre for Operational Research and Analysis, Ottawa ON (CAN)
The Canadian Forces make extensive use of strategic and tactical airlift assets to deploy and sustain overseas forces. Cargo aircraft are employed for missions to deliver equipment, supplies, and passengers. Maximizing the payload while maintaining a safe load balance is of high importance. In addition to safety considerations, proper load balancing also results in better fuel economy. 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, weight, volume, density, 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. A prototype model has been implemented as a software module named CABAL (Computer Aided Balanced Aircraft Loading) and tested on real-life instances.

Il y a un résumé en français ici.

Report Number
DRDC-CORA-TR-2008-004 — Technical Report
Date of publication
01 Nov 2008
Number of Pages
Electronic Document(PDF)

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