基于集合覆盖问题的应急物资储备库选址优化

Optimization of site selection for emergency-reserve warehouses based on the set covering problem

摘要

针对自然灾害频发背景下“黄金72小时”物资投送短板，构建兼顾效益与效率的储备库选址－分配双目标优化模型，对实现区域应急网络全覆盖、无盲区具有重要意义。本文以集合覆盖问题为框架，引入建设成本、运输成本与响应时效3个目标，建立多目标混合整数线性规划。设计“启用－分摊”联动约束与最小分摊比例，强制每需求点至少由L＝2座库协同供给(L表示每个需求点至少由L个储备库存供给)，提升稳健性。采用最小－最大归一化加权和法聚合目标，以Python优化建模对象(Python optimization modeling objects，Pyomo)结合GNU线性规划工具包(GNU linear programming kit，GLPK)精确求解。选取四川成都、德阳、绵阳38区县为实例，基于真实路网距离与人口需求完成仿真。在设定权重情景下，模型从38个候选点中优选9座储备库，构建“核心区高效供给＋边缘区兜底覆盖”的可解释网络，所有需求点均获至少双源协同供给。结果表明，该模型在可解释框架下实现了成本、时效与韧性的有效平衡，可为省级应急物资储备体系优化提供量化决策支持。

Abstract

To address the shortcomings in the “golden 72 hours” of material delivery during frequent natural disasters, this paper constructs a multi-objective optimization model for emergency reserve depot site selection and allocation that balances efficiency and effectiveness. This is crucial for achieving full coverage and eliminating blind spots in regional emergency networks. This paper uses a set coverage problem as a framework, introducing three objectives: construction cost, transportation cost, and response time. A multi-objective mixed-integer linear programming approach is established. To enhance the systemic robustness, an “activation-allocation” linkage constraint and a minimum allocation ratio is designed to force each demand point to be supplied by at least L=2 depots collaboratively (L denotes the number of depots supplying each demand point). The min-max normalization weighted sum method is used to aggregate the objectives, and the solution is obtained precisely using Pyomo (Python optimization modeling objects) and GLPK (GNU linear programming kit). A simulation is conducted using 38 districts and counties in Chengdu, Deyang, and Mianyang, Sichuan Province, based on real road network distances and population demand. Under a weighted scenario, the model selects 9 reserve depots from 38 candidate points, constructing an interpretable network of “efficient supply in the core area + backup coverage in the peripheral area”, ensuring that all demand points receive at least dual-source collaborative supply. The results show that the model achieves an effective balance between cost, timeliness and resilience within an interpretable framework, and can provide quantitative decision support for the optimization of provincial emergency material reserve systems.

关键词

应急物流 / 选址－分配模型 / 多目标优化 / 集合覆盖问题 / 韧性

Key words

emergency logistics / location-allocation model / multi-objective optimization / set covering problem / resilience

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基金资助

国家自然科学基金面上项目(72174019)

国家自然科学基金面上项目(72574017)

中央高校基本科研业务费研究生科技创新基金项目(ZY20260321)