In this paper, we address an extension of the classical two-dimensional bin packing (2BPP) that considers the spread of customer orders (2BPP-OS). The 2BPP-OS addresses a set of rectangular items, required from different customer orders, to be cut from a set of rectangular bins. All the items of a customer order are dispatched together to the next stage of production or distribution after its completion. The objective is to minimize the number of bins used and the spread of customer orders over the cutting process. The 2BPP-OS gains relevance in manufacturing environments that seek minimum waste solutions with satisfactory levels of customer service. We propose integer linear programming (ILP) models for variants of the 2BPP-OS that consider non-guillotine, 2-stage, restricted 3-stage, and unrestricted 3-stage patterns. We are not aware of integrated approaches for the 2BPP-OS in the literature despite its relevance in practical settings. Using a general-purpose ILP solver, the results show that the 2BPP-OS takes more computational effort to solve than the 2BPP, as it has to consider several symmetries that are often disregarded by the traditional 2BPP approaches. The solutions obtained by the proposed approaches have similar bin usage and significantly better metrics of customer satisfaction concerning the approaches that neglect the customer order spread.

在本文中，我们讨论了考虑客户订单分布的经典二维装箱（2BPP）的扩展（2BPP-OS）。 2BPP-OS 处理不同客户订单所需的一组矩形物品，这些物品需要从一组矩形箱中切割下来。客户订单的所有项目在完成后一起发送到下一阶段的生产或分销。目标是最大限度地减少切割过程中使用的箱子数量和客户订单的分布。 2BPP-OS 在寻求废物最少的解决方案和令人满意的客户服务水平的制造环境中获得了相关性。我们提出了针对 2BPP-OS 变体的整数线性规划 (ILP) 模型，该模型考虑非断头台、2 阶段、受限 3 阶段和无限制 3 阶段模式。尽管 2BPP-OS 在实际环境中具有相关性，但我们在文献中并未发现 2BPP-OS 的集成方法。使用通用 ILP 求解器，结果表明 2BPP-OS 比 2BPP 需要更多的计算工作量来求解，因为它必须考虑传统 2BPP 方法经常忽略的几个对称性。通过所提出的方法获得的解决方案具有类似的箱使用情况，并且对于忽略客户订单分布的方法而言，客户满意度指标明显更好。