A data-driven approach for mixed-case palletization with support

Palletization, a core activity in warehousing and distribution, involves the solution of a three-dimensional bin packing problem with side constraints. This problem is known as the mixed-case palletization problem. Motivated by the fact that solving industry-size instances is still very challenging for existing methodology, we propose a data-driven solution approach that combines data analysis at the instance level and optimization. For each instance, box heights are analyzed to identify possible layer heights and to derive relative positions of boxes. Boxes are then grouped in pairs and trios and stacked in stable arrangements called super-boxes. Using stable super-boxes of uniform height, a two-dimensional bin packing problem is solved to create layers of even height. The layers are then stacked on top of one another to create stable pallets. The layering approach combined with a careful layer and pallet formation leads to fully supported boxes. Computational tests on industry data demonstrate the efficiency of the approach in producing high-quality solutions in quick computational times, consistently placing around 80% of boxes in layers, achieving an average pack density of 84%, and attaining full support for more than 99% of boxes.