Integrated train scheduling and dynamic pricing with endogenous demand under uncertainty: A machine learning-enhanced Benders decomposition approach

Abstract

This study develops an integrated optimization framework for mitigating crowding in urban rail transit systems through the joint design of train scheduling, dynamic pricing, passenger arrival time shifting, and passenger flow control under demand uncertainty. Unlike conventional studies that treat time-varying demand as exogenous, we explicitly model fare-dependent passenger arrival time choice. The problem is formulated as a stochastic program that minimizes total passengers’ travel time subject to train capacity limits, service priority for reserved passengers, and a government subsidy budget. To solve the model, we develop an improved Benders decomposition method further enhanced by machine learning. Numerical results show that the proposed approach effectively reduces passengers’ waiting time and improves computational efficiency.