This paper introduces a methodology designed to reduce cost, improve demand coverage, and ensure equitable vaccine distribution during the initial stages of the vaccination campaign when demand significantly exceeds supply. We formulate an enhanced maximum covering problem as a mixed integer linear program, aiming to minimize the total vaccine distribution cost while maximizing the allocation of vaccines to population blocks under equity constraints. Block‐level census data are employed to define demand locations, identifying gender, age, and racial groups within each block using population data. A Lagrangian relaxation technique integrated with a modified Voronoi diagram is proposed to solve the location–allocation problem efficiently. Empirical case studies in Pennsylvania, using real‐world data from the Centers for Disease Control and Prevention and health department websites, were conducted for the first 4 months of the COVID‐19 vaccination campaign. Preliminary results show that the proposed solution algorithm effectively solves the problem, achieving a 5.92% reduction in total transportation cost and a 28.15% increase in demand coverage. Moreover, our model can reduce the deviation from equity to 0.07 (∼50% improvement).

中文翻译：

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用于公平资源分配的基于松弛的 Voronoi 图方法


本文介绍了一种方法，旨在降低成本，提高需求覆盖率，并确保在疫苗接种运动的初始阶段（当需求显着超过供应时）公平分配疫苗。我们将增强的最大覆盖问题制定为混合整数线性规划，旨在最小化总疫苗分配成本，同时在公平约束下最大化疫苗分配到人口块。街区级人口普查数据用于定义需求地点，并使用人口数据识别每个街区内的性别、年龄和种族群体。提出了一种与改进的 Voronoi 图相结合的拉格朗日松弛技术来有效地解决位置分配问题。使用来自疾病控制与预防中心和卫生部门网站的真实数据，在宾夕法尼亚州开展了 COVID-19 疫苗接种活动的前 4 个月的实证案例研究。初步结果表明，所提出的解决算法有效解决了问题，实现了总运输成本降低5.92%，需求覆盖率提高28.15%。此外，我们的模型可以将权益偏差减少到 0.07（~50% 的改进）。