In this paper, we address the problem of automating the definition of feasible pallets configurations. This issue is crucial for the competitiveness of logistic companies and is still one of the most difficult problems in internal logistics. In fact, it requires the fast solution of a three-dimensional Bin Packing Problem (3D-BPP) with additional logistic specifications that are fundamental in real applications. To this aim, we propose a matheuristics that, given a set of items, provides feasible pallets configurations that satisfy the practical requirements of items’ grouping by logistic features, load bearing, stability, height homogeneity, overhang as well as weight limits, and robotized layer picking. The proposed matheuristics combines a mixed integer linear programming (MILP) formulation of the 3D-Single Bin-Size BPP (3D-SBSBPP) and a layer building heuristics. In particular, the feasible pallets configurations are obtained by sequentially solving two MILP sub-problems: the first, given the set of items to be packed, aims at minimizing the unused space in each layer and thus the number of layers; the latter aims at minimizing the number of shipping bins given the set of layers obtained from the first problem. The approach is extensively tested and compared with existing approaches. For its validation we use both realistic data-sets drawn from the literature and real data-sets, obtained from an Italian logistics leader. The resulting outcomes show the effectiveness of the method in providing high-quality bin configurations in short computational times. Note to Practitioners—This work is motivated by the intention of facilitating the transition from Logistics 3.0 to Logistics 4.0 by providing an effective tool to automate bin packing, suitable for automated warehouses. On the one hand, the proposed technique provides stable and compact bin configurations in less than half a minute per bin on average, despite the high computational complexity of the 3D-SBSBPP. On the other hand, the approach allows to consider compatibility constraints for the items (e.g., final customer and category of the items), and the use of robotized layer picking in automated warehouses. In effect, layers composed by only one type of items (i.e., monoitem layers) can be directly picked and placed on the pallet by a robotic arm without the intervention of any operator. Consequently, the adoption of this approach in warehouses could drastically improve the efficiency of the packing process.

中文翻译：

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自动化装箱：构建具有成本效益的物流数学层


在本文中，我们解决了自动定义可行托盘配置的问题。这一问题对于物流企业的竞争力至关重要，并且仍然是内部物流中最困难的问题之一。事实上，它需要快速解决三维装箱问题（3D-BPP）以及实际应用中至关重要的附加物流规范。为此，我们提出了一种数学方法，给定一组物品，提供可行的托盘配置，满足物品按物流特征、承载、稳定性、高度均匀性、悬垂和重量限制分组的实际要求，以及机器人化层拾取。所提出的数学方法结合了 3D-Single Bin-Size BPP (3D-SBSBPP) 的混合整数线性规划 (MILP) 公式和层构建启发法。具体来说，可行的托盘配置是通过顺序解决两个 MILP 子问题获得的：第一个，给定要包装的物品集，旨在最小化每层中未使用的空间，从而最小化层数；后者的目的是在给定从第一个问题获得的层集的情况下最大限度地减少运输箱的数量。该方法经过广泛测试并与现有方法进行比较。为了进行验证，我们使用从文献中提取的实际数据集和从意大利物流领导者那里获得的真实数据集。结果表明该方法在短时间内提供高质量箱配置的有效性。从业者须知——这项工作的目的是促进从物流 3.0 到物流 4 的过渡。0 通过提供有效的自动化装箱工具，适用于自动化仓库。一方面，尽管 3D-SBSBPP 的计算复杂度很高，但所提出的技术平均每个 bin 不到半分钟即可提供稳定且紧凑的 bin 配置。另一方面，该方法允许考虑物品的兼容性约束（例如，最终客户和物品类别），以及在自动化仓库中使用机器人层拣选。实际上，仅由一种类型的物品（即单物品层）组成的层可以通过机械臂直接拾取并放置在托盘上，而无需任何操作员的干预。因此，在仓库中采用这种方法可以大大提高包装过程的效率。