一种选择最佳装箱尺寸的决策树框架
A decision-tree framework to select optimal box-sizes for product shipments
摘要：
在包裹处理设施中，不同尺寸的箱子用于运输产品。具有比产品尺寸大得多的箱尺寸的不适当尺寸的箱产生浪费并且不适当地增加运输成本。由于不可能为每种$N$产品制作独特的定制包装盒，因此电子商务公司面临的基本问题是：需要制造多少个$K << N$立方体包装盒以及它们的尺寸应该是多少？在本文中，我们提出了一个解决方案，用于每箱包含一个产品的单次计数装运，分为两个步骤：（i）将其简化为长度、宽度和高度的$3$维空间中的聚类问题，其中每个聚类对应于将以特定尺寸变体装运的产品组，提出了一种基于前向-后向决策树的低计算复杂度的$N$和$K$聚类方法，得到了这些$K$簇和相应的盒维数。我们的算法有多个组成部分，每个部分都是专门设计来实现高质量的聚类解决方案的。由于我们的方法以增量方式生成集群，而不会丢弃当前的解决方案，因此添加或删除大小变量就像提前停止向后传递或再执行一次迭代一样简单。我们测试了我们的方法的有效性，通过模拟实际的单次计数的货物运输在一个月内由亚马逊使用拟议的盒子尺寸。即使只是修改现有的包装箱尺寸，而不添加新的尺寸变体，我们也实现了运输量减少$4.4\%$，从而使未利用的空气体积空间减少了$2.2\%$。当我们引入额外的$4$包装盒时，$10.3\%$和$6.1\%$的运输量和空气量的减少显著改善。
英文摘要：
In package-handling facilities, boxes of varying sizes are used to ship products. Improperly sized boxes with box dimensions much larger than the product dimensions create wastage and unduly increase the shipping costs. Since it is infeasible to make unique, tailor-made boxes for each of the $N$ products, the fundamental question that confronts e-commerce companies is: How many $K << N$ cuboidal boxes need to manufactured and what should be their dimensions? In this paper, we propose a solution for the single-count shipment containing one product per box in two steps: (i) reduce it to a clustering problem in the $3$ dimensional space of length, width and height where each cluster corresponds to the group of products that will be shipped in a particular size variant, and (ii) present an efficient forward-backward decision tree based clustering method with low computational complexity on $N$ and $K$ to obtain these $K$ clusters and corresponding box dimensions. Our algorithm has multiple constituent parts, each specifically designed to achieve a high-quality clustering solution. As our method generates clusters in an incremental fashion without discarding the present solution, adding or deleting a size variant is as simple as stopping the backward pass early or executing it for one more iteration. We tested the efficacy of our approach by simulating actual single-count shipments that were transported during a month by Amazon using the proposed box dimensions. Even by just modifying the existing box dimensions and not adding a new size variant, we achieved a reduction of $4.4\%$ in the shipment volume, contributing to the decrease in non-utilized, air volume space by $2.2\%$. The reduction in shipment volume and air volume improved significantly to $10.3\%$ and $6.1\%$ when we introduced $4$ additional boxes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
