Ethiopia's Ministry of Health is upgrading health posts to improve access to essential services, particularly in rural areas. Limited resources, however, require careful prioritization of which facilities to upgrade to maximize population coverage while accounting for diverse expert and stakeholder preferences. In collaboration with the Ethiopian Public Health Institute and Ministry of Health, we propose a hybrid framework that systematically integrates expert knowledge with optimization techniques. Classical optimization methods provide theoretical guarantees but require explicit, quantitative objectives, whereas stakeholder criteria are often articulated in natural language and difficult to formalize. To bridge these domains, we develop the Large language model and Extended Greedy (LEG) framework. Our framework combines a provable approximation algorithm for population coverage optimization with LLM-driven iterative refinement that incorporates human-AI alignment to ensure solutions reflect expert qualitative guidance while preserving coverage guarantees. Experiments on real-world data from three Ethiopian regions demonstrate the framework's effectiveness and its potential to inform equitable, data-driven health system planning.

翻译：埃塞俄比亚卫生部正在升级卫生站，以改善基本服务的可及性，特别是在农村地区。然而，有限的资源要求对升级哪些设施进行审慎的优先排序，以在考虑不同专家和利益相关者偏好的同时，最大化人口覆盖范围。在与埃塞俄比亚公共卫生研究所和卫生部的合作中，我们提出了一个混合框架，系统地将专家知识与优化技术相结合。经典优化方法提供了理论保证，但需要明确、量化的目标，而利益相关者的标准通常以自然语言表述，难以形式化。为了弥合这两个领域，我们开发了大语言模型与扩展贪心算法框架。该框架将一种用于人口覆盖优化的可证明近似算法与基于大语言模型的迭代优化相结合，通过人机对齐确保解决方案反映专家的定性指导，同时保持覆盖保证。在埃塞俄比亚三个地区的真实数据上进行的实验证明了该框架的有效性及其为公平、数据驱动的卫生系统规划提供信息的潜力。