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.

码垛是仓储和配送的核心活动，涉及解决具有侧面约束的三维装箱问题。这个问题被称为混合货箱托盘化问题。由于解决行业规模的实例对于现有方法仍然非常具有挑战性，因此我们提出了一种数据驱动的解决方案，将实例级别的数据分析和优化相结合。对于每个实例，分析框高度以识别可能的层高度并导出框的相对位置。然后将盒子成对和三重组合在一起，并以称为超级盒子的稳定排列堆叠。使用均匀高度的稳定超级盒子，解决二维装箱问题以创建均匀高度的层。然后将这些层堆叠在一起以形成稳定的托盘。分层方法结合仔细的层和托盘形成导致完全支持的箱子。对行业数据的计算测试证明了该方法在快速计算时间内生成高质量解决方案的效率，一致地将大约 80% 的盒子分层放置，实现了 84% 的平均包装密度，并获得了超过 99% 的完全支持的盒子。