MIP-based constructive heuristics for the three-dimensional Bin Packing Problem with transportation constraints

This article is about seeking a good feasible solution in a reasonable amount of computation time to the three-dimensional Multiple Bin Size Bin Packing Problem (MBSBPP). The MBSBPP studied considers additional constraints encountered in real world air transportation situations, such as cargo stability and the particular shape of containers. This MBSBPP has already been formulated as a Mixed Integer linear Programming problem, but as yet only poor results have been achieved for even fairly small problem sizes. The goal of the work this paper describes is to develop heuristics that are able to quickly provide good initial feasible solutions for the MBSBPP. Three methodologies are considered, which are based on the decomposition of the original problem into easier subproblems: the matheuristics Relax-and-Fix, Insert-and-Fix and Fractional Relax-and-Fix. They have been parametrised on real data sets and then compared to each other. In particular, two of these techniques show promising results in reasonable computational times.