A tailored two-phase constructive heuristic for the three-dimensional Multiple Bin Size Bin Packing Problem with transportation constraints

This paper considers the three-dimensional Multiple Bin Size Bin Packing Problem which
consists in packing a set of cuboid boxes into containers of various shapes with minimising
unused space. The problem is extended to air cargo where bins are Unit Load Devices,
especially designed for fitting in aircraft. We developed a fast constructive heuristic able to
manage the different constraints met in transportation. The heuristic is split into two distinct
phases. The first phase deals with the packing of boxes into identical bins using an extension
of the Extreme Points. During this phase, the fragility, stability and orientations of the boxes
are taken into account as well as the special shape of the bins and their weight capacity.
The second phase takes into account the multiple types of available bins. If necessary, the
best found loading pattern is finally enhanced with respect to weight distribution in a post
processing. After parametrisation, computational experiments have been performed on data
sets especially designed for this application. The heuristic requires really short computational
times to achieve promising results.