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, while minimising unused space. The problem is extended to air cargo where the bins are Unit Load Devices, specially designed for fitting in aircraft. We developed a fast constructive heuristic able to manage the constraints to be 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 which describe the possible interesting positions to accommodate boxes. During this phase, the fragility, stability and orientation of the boxes are taken into account as well as the special shape of the bins and their weight capacity. The second phase considers the multiple types of available bins. If necessary, the best loading pattern identified is enhanced with respect to weight distribution in post processing. After the description of the parametrisation, computational experiments are performed on data sets specially designed for this application. The heuristic requires only few seconds to achieve promising results in terms of filling rate.