电商履约中心的箱体尺寸规划的维度分解与列生成
Dimensional Decomposition and Column Generation for Bin Dimensioning in E-Commerce Fulfillment Centers
- Instituto Tecnológico de Aeronáutica (ITA)（巴西航空技术研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对电商履约中心的箱体尺寸规划问题，提出维度分解将三维装箱简化为块定位，结合BFD启发式和列生成求解，实验验证了可扩展性与紧下界。
AI中文摘要：
履约中心（FC）是一种专门的物流设施，用于接收、存储和处理电商库存。其内部组织直接影响空间利用率以及上架和拣选作业的性能。物品按照严格的操作指南存储在箱体中，以确保这两项活动的生产率，因此箱体尺寸必须针对每个设施的产品特征进行定制，以最大化空间利用率。我们研究了电商履约中心中出现的箱体尺寸规划问题：给定一组候选箱体类型和大量异构库存，确定每种类型的箱体数量，并在遵守关于产品如何在单个箱体内组合的操作约束的前提下，将所有物品分配出去，以最小化总箱体体积。我们开发了一种维度分解方法，利用这些约束将三维装箱问题简化为一个一维块定位问题。基于这种分解，我们将该问题表述为一个混合整数线性规划，并提出了两种求解方法：一种最佳适配递减（BFD）启发式算法和一种产生紧的线性规划下界的列生成方案。在四个合成数据集上的计算实验（这些数据集根据一家美国电商金融科技公司的专有数据校准，规模从1.5千到150万个SKU不等）表明，BFD启发式算法可扩展到多达170万个块的实例，并且列生成在最小数据集上证明了BFD与LP之间的间隙为2.26%。实验进一步揭示了各数据集之间解质量的结构性差异，这种差异由操作约束与每个设施产品特征之间的相互作用驱动。
英文摘要：
A fulfillment center (FC) is a specialized logistics facility where e-commerce inventory is received, stored, and processed. Its internal organization directly impacts space utilization and the performance of put-away and picking operations. Items are stored in bins following strict operational guidelines to ensure productivity in both activities, so bin dimensions must be tailored to the product profile of each facility to maximize space utilization. % We address the bin dimensioning problem arising in e-commerce fulfillment centers: given a set of candidate bin types and a large, heterogeneous inventory, determine the number of bins of each type and assign all items so as to minimize total bin volume, subject to operational constraints governing how products may be combined within a single bin. We develop a dimensional decomposition that exploits these constraints to reduce the three-dimensional packing problem to a one-dimensional block-positioning problem. Building on this decomposition, we formulate the problem as a mixed-integer linear program and propose two solution methods: a Best-Fit-Decreasing (BFD) heuristic and a column generation scheme that produces tight LP lower bounds. Computational experiments on four synthetic datasets, calibrated on proprietary data from an American e-commerce fintech and ranging from 1.5 thousand to 1.5 million SKUs, show that the BFD heuristic scales to instances with up to 1.7 million blocks, and that column generation certifies a BFD--LP gap of 2.26\% on the smallest dataset. The experiments further reveal a structural divide in solution quality across datasets, driven by the interaction between operational constraints and each facility's product profile.
