Operational multistage nonlinear inefficiency and regime exploration - An empirical benchmarking of Indian Railways

Indian Railways is the nation's backbone and largest public sector entity. In a rapidly expanding and emerging economy, it faces unprecedented operational challenges. This study conducts an in-depth route-level efficiency analysis using a five-stage empirical approach. A large real-time dataset of 267 trains from the Southern Railways, comprising daily occupancy and enriched features over 2 years and 10 months from April 2022 to February 2025, is used. Data Envelopment Analysis provides 267 efficiency scores based on 21 input factors and 9 occupancy-based output variables. A fractional logit model connects efficiency scores to standard operational parameters. The authors then adopt a representation learning and clustering approach to determine structural heterogeneity. A Variational Autoencoder is employed to learn low-dimensional representations of operational features. The latent representations obtained are further projected using Uniform Manifold Approximation and Projection. Finally, operational archetypes are generated from the latent space using density-based clustering. The methodology uniquely combines non-parametric efficiency measurement with advanced visual exploration to identify service-level structural variability. The results indicate that 85.27% of the routes are efficient under Variable Returns to Scale. Coach diversity, not average speed or scheduling complexity, is the most important positive driver. Challenging operational conditions, including elevation, night arrivals or departures, and weekday or weekend schedules, did not seem to slow down overall service efficiency. Policymakers and railway operators can formulate route-specific interventions using this analytical and visual framework. Further, it makes it possible to systematically improve resource allocation and service design without having to use the same measurements across the whole network.