Cities deliver basic services through mixed public-private facility networks, including schools, clinics, transit providers, and subsidized service points. In these systems, planners often observe where households go, but not the latent cost function through which they trade off factors such as distance, price, and institutional access. We study this urban problem through school choice in the Philippines, where the country's largest national education subsidy is intended to redirect learners from congested public schools to participating private schools. 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 through a differentiable Sinkhorn forward pass. Applied to 283{,}016 learner trips across 23{,}820 observed flows in the most populated region, the framework estimates a subsidy-equivalent distance, $λ^{(k)}$, interpreted as the kilometers of perceived travel cost offset by the subsidy. The case demonstrates how administrative origin-destination data can be transformed into interpretable planning metrics for accessibility-aware subsidy design, facility siting, and urban service allocation.

翻译：城市通过公私混合设施网络提供基本服务，包括学校、诊所、交通服务提供者和补贴服务点。在这些系统中，规划者通常能观察到家庭的目的地，却无法了解他们权衡距离、价格和机构可达性等要素的潜在成本函数。我们通过菲律宾的学校选择问题研究这一城市问题：该国最大的国家教育补贴旨在将学生从拥挤的公立学校引导至参与计划的私立学校。将学校间的注册流动视为熵正则化最优传输方案，我们利用两种互补的逆最优传输模型恢复潜在选择成本：一种包含补贴项的可解释距离分段模型，以及一种通过可微分的Sinkhorn前向传播训练的神经成本模型。将该框架应用于该国人口最密集地区23,820条观测流动中的283,016次学生出行，模型估计出补贴等效距离$λ^{(k)}$，该参数可解释为补贴所抵消的感知旅行成本对应的公里数。该案例展示了如何将行政起点-终点数据转化为可解释的规划指标，用于促进可达性的补贴设计、设施选址和城市服务分配。