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What is OR ?


Air cargo management

This project was developed by Sabine Limbourg (HEC-ULg, QuantOM), Michaël Schyns (HEC-ULg, QuantOM) and Gilbert Laporte (HEC Montréal, CIRRELT).The details are provided in their paper "Automatic Aircraft Cargo Loading", Journal of the Operational Society, DOI 10.1057/jors.2011.134 .

Links: Air cargo mgt & team - W&B problem - Our solution & video - Download - Additional information

Model and optimization

Mathematical modelLet us consider a common case: a 747-400 Boeing with 77 available positions to be loaded with a shipment of 67 ULDs. This is a combinatorial problem with a very large number of solutions to consider. In theory, we should check 4E106 different allocations for feasibility and optimality! Fortunately, Operations Research provides efficient tools and methods.

The scientific contribution of our approach is the development of an integer linear programming model for the aircraft load planning problem. Our model can handle all constraints of the problem.


We have also developed a software that takes as input all of the problem's data and feeds them to the IBM ILOG CPLEX integer linear programming solver through the proposed model.

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High Definition version

Our software is written in Java and runs on any computers. Tests were carried out on a set of real instances suggested by one of our partners. It is shown that feasible and optimal solutions can be reached within a few seconds only. Our solutions were compared to those obtained by an experienced loadmaster and shown to be at least as good in every respect. Moreover, the software allows the load- master to accept the solution or to iteratively restart the optimization after restricting any ULDs to specific positions in order to take into account more complex problems.

Links: Air cargo mgt & team - W&B problem - Our solution & video - Download - Additional information

  HEC-Management School - University of Liège