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Health Facility Location in Ethiopia: Leveraging LLMs to Integrate Expert Knowledge into Algorithmic Planning

Yohai Trabelsi, Guojun Xiong, Fentabil Getnet, Stéphane Verguet, Milind Tambe

TL;DR

The paper tackles equitable health-access planning in Ethiopia under budget constraints by marrying submodular optimization with Large Language Model (LLM) reasoning. It introduces the LEG framework, an adaptive, LLM-guided refinement loop that preserves provable coverage guarantees while integrating expert qualitative guidance through an α–β controlled trade-off. The approach is theoretically grounded and validated on real regional data, demonstrating improved alignment with expert advice without sacrificing population coverage, and it supports online budgeting for multi-year planning. By providing a transparent, human-aligned optimization pipeline, the work offers a practical blueprint for data-driven, context-aware health system planning. The methodology extends beyond health facilities to other resource-allocation problems requiring both quantitative performance and qualitative stakeholder alignment.

Abstract

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.

Health Facility Location in Ethiopia: Leveraging LLMs to Integrate Expert Knowledge into Algorithmic Planning

TL;DR

The paper tackles equitable health-access planning in Ethiopia under budget constraints by marrying submodular optimization with Large Language Model (LLM) reasoning. It introduces the LEG framework, an adaptive, LLM-guided refinement loop that preserves provable coverage guarantees while integrating expert qualitative guidance through an α–β controlled trade-off. The approach is theoretically grounded and validated on real regional data, demonstrating improved alignment with expert advice without sacrificing population coverage, and it supports online budgeting for multi-year planning. By providing a transparent, human-aligned optimization pipeline, the work offers a practical blueprint for data-driven, context-aware health system planning. The methodology extends beyond health facilities to other resource-allocation problems requiring both quantitative performance and qualitative stakeholder alignment.

Abstract

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.
Paper Structure (43 sections, 2 theorems, 11 equations, 10 figures, 1 table, 3 algorithms)

This paper contains 43 sections, 2 theorems, 11 equations, 10 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Process description
  3. Contributions
  4. Related Works
  5. Plan-and-execute
  6. Multi-objective optimization
  7. Using LLMs for reward shaping
  8. Health facility location
  9. Human-AI alignment
  10. Settings and Problem Formulation
  11. Settings
  12. Coverage function.
  13. Advice alignment function.
  14. Problem Formulation
  15. The multi-objective problem.
  16. ...and 28 more sections

Key Result

theorem 1

Let $b \in \mathbb{N}_{>0}$ and $\alpha, \beta \in [0,1]$ be the input parameters to Algorithm alg:1. Let $OPT_b \subseteq \mathcal{V}$ denote an optimal subset of size $b$ maximizing $f$. Denote by $S_{\text{limit}}$ the allocation returned by Algorithm alg:1. Then

Figures (10)

  • Figure 1: Basic health post (left); Design of a comprehensive health post that provides more essential services (right). Health Extension Program (HEP) report, Ministry of Health.
  • Figure 2: (choo2026optimizing) Map of Ethiopia overlaid with projected population estimates for 2026 (log scale). Brighter yellow areas on the left indicate higher population densities. The map on the right shows the locations of health facilities capable of providing essential health services (red points). Many populations currently lack 2-hour access to such facilities hendrix2023estimated.
  • Figure 3: Overview of the proposed method.
  • Figure 4: Toy running example with two districts and four cells; For GuidedGreedy, we use the parameters $\alpha=0,\beta=1$ allowing the LLM to fully determine the district allocation. Greedy() denotes the greedy algorithm of nemhauser1978analysis.
  • Figure 5: Verbal vs quantitative for Afar; $\alpha=0.0$, $\beta=1.0$.
  • ...and 5 more figures

Theorems & Definitions (6)

  • Remark 1: Challenges of multi-objective optimization
  • Remark 2: A heuristic improvement for $\beta=1.0$
  • theorem 1
  • theorem 2
  • Remark 3
  • Remark 4