A constructive heuristic for the three dimensional Bin Packing Problem with transportation constraints

The aim of this work is to propose a Relax-And-Fix heuristic to build a good initial solution to the 3D BPP. First, a mathematical formulation has been developed taking into account several types of constraints such as the stability and fragility of the boxes to pack, their possibility to rotate, the weight distribution inside the bins and their special shapes. Since this model contains a lot of integer variables, we have decided to apply the Relax-and-Fix method. We have selected several sets of variables to be the branching variables and carried out some tests.