Cities provide basic services through mixed public-private facility networks, including schools, clinics, transit providers, and subsidized service points. In these systems, planners often observe household movements but lack insight into the latent cost function that balances factors such as distance, price, and institutional access. We examine this urban issue through school choice in the Philippines, where the largest national education subsidy aims to redirect learners from congested public schools to participating private schools.
By treating school-to-school enrollment flows as an entropic optimal transport plan, we recover latent choice costs using two complementary inverse optimal transport models: an interpretable distance-banded model with a subsidy term, and a neural cost model trained via a differentiable Sinkhorn forward pass. Applied to 283,016 learner trips across 23,820 observed flows, the framework estimates a subsidy-equivalent distance, $\lambda^{(k)}$, interpreted as the kilometers of perceived travel cost offset by the subsidy. This case illustrates how administrative origin-destination data can be transformed into interpretable planning metrics for accessibility-aware subsidy design, facility siting, and urban service allocation.
Blogger's Review: This study innovatively reveals the latent costs of urban services through inverse optimal transport models, particularly in the context of educational resource allocation, offering a data-driven approach to urban planning that provides significant insights for policymakers.