Multi-objective 3D bin-packing problem

This research paper deals with a special case of a multiobjective 3D-Bin Packing Problem. n 3D boxes of different volumetric dimensions are to be filled in a minimum number of identical bins. The boxes have different weights and can be only horizontally rotated when placed in the bins. Two objectives are simultaneously considered: Use the minimum number of bins to pack all the boxes and have balanced bins in term of total weight. The investigated problem is NP-hard. A 3D algorithm is proposed to solve this problem in two main phases. During the first phase, all the possible combinations of layers of same or different types of boxes that can fit in a bin are generated. These combinations represent candidate solutions in term of bin's volume. Finally, in the second phase the boxes are packed in the bins according to the best use of the bin's volume from the solutions candidates. This 3D algorithm was validated using real world data from the courier company Fedex and compared with the results of a lower bound and another recently published algorithm. The results showed that the proposed algorithm is much better in both criteria.