电商仓储缺货损失与库存成本协同优化——基于共轭梯度法的帕累托前沿求解

Collaborative Optimization of Stockout Loss and Inventory Cost in E-Commerce Warehouses—Pareto Frontier Solution Based on Conjugate Gradient Method

摘要: 在供应链快速发展与电商需求高波动背景下，库存缺货损失与运营成本的权衡成为电商仓储管理的核心难题。本文针对随机需求与固定补货提前期场景，构建以最小化年期望缺货损失、最小化总库存运营成本为双目标的库存优化模型，以安全库存系数与订货批量为决策变量，通过对数变换将原问题转化为无约束光滑向量优化问题，并采用多目标共轭梯度法结合强Wolfe线搜索求解帕累托前沿。基于Kaggle物流仓储数据集进行参数标定与数值实验，得到35个非支配帕累托最优解，结果表明缺货损失与库存成本随服务水平提升呈边际递增替代关系，且模型在参数±20%扰动下具有良好稳定性。依据帕累托前沿将决策方案划分为高服务保障、均衡稳健、低成本运营三类区间，提出商品差异化履约、精益补货、大促弹性调度及缺货成本优先标定等实操策略，可为电商企业从经验式补货转向数据驱动、动态优化的精细化库存管理提供量化方法与决策支撑，助力企业在库存成本、资金周转与客户服务体验之间实现科学均衡。

Abstract: Against the background of rapid supply chain development and highly volatile e-commerce demand, the trade-off between stockout loss and operating cost has become a core issue in e-commerce warehouse management. This paper addresses the scenario of stochastic demand and fixed replenishment lead time, and constructs a bi-objective inventory optimization model aiming to minimize the annual expected stockout loss and the total inventory operating cost. Taking the safety stock coefficient and order quantity as decision variables, the original problem is transformed into an unconstrained smooth vector optimization problem through logarithmic transformation. A multi-objective conjugate gradient method combined with strong Wolfe line search is adopted to solve the Pareto frontier. Based on the Kaggle logistics warehouse dataset, parameter calibration and numerical experiments are carried out, and 35 non-dominated Pareto optimal solutions are obtained. The results show that the stockout loss and inventory cost exhibit a marginally increasing substitution relationship as the service level improves, and the model remains robust under ±20% parameter perturbations. According to the Pareto frontier, the decision schemes are divided into three categories: high service guarantee, balanced robustness, and low-cost operation. Practical strategies such as differentiated commodity fulfillment, lean replenishment, elastic inventory scheduling during promotion periods, and prior calibration of stockout cost are proposed. This study can provide quantitative methods and decision support for e-commerce enterprises to transform from empirical replenishment to data-driven and dynamically optimized refined inventory management, helping them achieve a scientific balance among inventory cost, capital turnover and customer service experience.