摘要：

为保证包括公共卫生事件在内的灾后物资供应, 合理制定预防性的物资仓储选址和仓储网络中的物资分布策略至关重要。面向灾后需求分布不确定情境, 研究一类多种类应急物资仓储分布模型。基于有限历史样本数据, 制定一个包含关于灾前随机因素部分信息的模糊集合, 构建两阶段物资仓储调度规划的分布鲁棒优化模型, 以最小化模糊集合中定义的所有分布下的成本期望值为优化目标。模型包括仓储网络规划和物资调度分配的两阶段协同优化, 阶段一针对需求分布不确定的预防性仓库选址与物资预储备问题, 阶段二对仓储网络中的应急物资调度分配进行规划。针对模型求解, 通过应用一类对偶方法将非线性分布鲁棒优化转化为线性优化, 并设计一类拉格朗日L形方法(LLSM)对两阶段模型进行求解。通过构造算例集合对模型和算法的鲁棒性进行验证, 并分析仓储网络选址和物资分布决策对不同级别灾害后物资缺口的敏感性。

关键词: 应急物资规划, 不确定场景, 分布鲁棒优化, 两阶段模型, 拉格朗日L形算法

Abstract:

A reasonable preventive strategy for the location and distribution of emergency materials within a logistics network is key to ensuring the supply of materials after urgent events, such as the recent public health crisis. This paper investigates a class of multi-category emergency material storage distribution models under scenarios with uncertain post-event demand distribution. Based on limited historical sample data, a fuzzy set containing information about random factors before a disaster is established, and a distributionally robust optimization model of two-stage material planning is constructed, with the optimization goal of minimizing the expected cost under all distributions defined in the fuzzy set. The model includes two stages of collaborative optimization: warehouse network planning, and material scheduling and distribution. The first stage focuses on the problem of preventive warehouse location and material pre-storage with an uncertain demand distribution. The second stage plans emergency material scheduling and distribution in the warehouse network. Nonlinear distributionally robust optimization is transformed into linear optimization by applying a dual method, and a Lagrangian L-Shaped Method (LLSM) is designed to solve the two-stage model. The robustness of the model and algorithm is verified by constructing an example set, and the sensitivity of warehouse network location and material distribution decision in addressing material gaps after different levels of disasters is analyzed.

Key words: emergency material planning, uncertain scenarios, distributionally robust optimization, two-stage model, Lagrangian L-Shaped Method (LLSM)