Integrated train timetable with supply–demand interactions at the Chinese high-speed railway

In traditional Chinese railway operations, train timetable and unit assignment are usually separated from pricing and seat allocation, resulting in a decrease in revenue and an increase in operating costs. In this paper, we study the integrated problem of train timetable, unit assignment, pricing, and seat allocation, where passenger choice behavior is modeled by the multinomial logit (MNL) model. This integration enables us to explicitly capture supply–demand interactions. The problem is formulated as a mixed integer nonlinear programming model with the objective of maximizing total profit. By converting the MNL model into its equivalent convex form, we recast the model as a tractable reformulation, allowing the use of a general-purpose solver to solve practical-sized instances. Based on real data from high-speed railway lines in China, three sets of case studies are conducted to validate the effectiveness and efficiency of the proposed approach.