# Impact of linear programming-based optimization of pediatric hospital location and quantity on patient travel time in Germany

## TL;DR

This study shows that optimizing the placement of pediatric hospitals in Germany using linear programming can significantly reduce patient travel times and improve access to care.

## Contribution

The paper introduces a linear programming method to optimize hospital allocation, demonstrating its effectiveness in improving pediatric care accessibility.

## Key findings

- Linear programming reduced weighted median travel time by 5.5% and unweighted median by 15.0%.
- The proportion of patients exceeding the 40-minute travel threshold dropped by 36.1% with optimized allocation.
- Optimization had greater benefits in rural areas and when increasing the number of hospitals.

## Abstract

Access to pediatric medical care is a critical factor in determining health outcomes. Hospital landscape restructuring processes need to consider the geographical accessibility of pediatric emergency and inpatient services. Public regulators in Germany aim for a travel time to the closest pediatric emergency hospital below a threshold of 40 min. This study investigates whether optimizing the allocation of pediatric hospital services to existing hospital sites by different approaches can improve accessibility by reducing travel time and enhancing threshold compliance.

We analyzed patient travel time by car to the nearest pediatric hospital using a comprehensive dataset of all hospitals in Germany, weighted by population density. Two optimization approaches were applied to minimize travel time by reallocating pediatric health services to existing hospital locations, k-means clustering and a p-median optimization method based on linear programming. We further evaluated the impact of adjusting the quantity of location-optimized pediatric hospitals on patient travel time.

Allocation optimization using linear programming reduced weighted median travel time by 5.5% (p < 0.0001), unweighted median travel time by 15.0% (p < 0.0001) and the proportion of patients with travel time exceeding 40 min by 36.1%. Travel time improvement using k-means clustering algorithm was less pronounced. Location optimization led to greater gains in compliance with the 40 minute threshold in rural than in urban areas. Quantity of hospitals was inversely associated with travel time length and proportion of patients with travel time above 40 min threshold. In a model that prioritized existing pediatric hospital locations, increasing the number of hospitals led to more marked travel time changes than decreasing hospital quantity.

The study highlights the potential of linear programming as an approach for optimizing countrywide hospital service allocation to enhance geographical accessibility of specialized care. It emphasizes the necessity of considering optimization methods for restructuring healthcare infrastructure and provides a model that may facilitate planning processes at a supra-regional or countrywide scale.

The online version contains supplementary material available at 10.1186/s12913-026-14042-y.