Integrated optimization of flexible train timetable, stop plan and exogenous passenger assignment under demand responsive condition

Demand responsive bus has been put into practice widely in recent decades. However, implementing this concept in railway transportation poses considerable challenges. One of the main obstacles is how to synchronize train timetable, stop plan, and passenger assignment to guarantee the interests of the operators and passengers. Additionally, it is crucial to fulfill various operational requirements under resource constraints and address the issue of supply-demand mismatch. This paper introduces an integrated optimization model incorporating a flexible train timetable, stop plan, and exogenous passenger assignment based on demand responsiveness. Realistic situations, such as overtaking, no preset train departure time window, and allowing passengers’ requests to be rejected, are considered. Leveraging data from the trip reservation system (TRS), we aim to maximize enterprise operating profit while minimizing passenger travel costs. To achieve this, we embed the train stop plans and passenger assignment constraints into the train timetable, introduce the reservation rolling horizon, and establish a multi-objective mixed-integer nonlinear programming (MINLP) model. We employ the GUROBI optimization solver to obtain optimal or near-optimal solutions for our proposed model. Numerical and real-world cases are conducted to demonstrate the performance of the proposed method. The experimental results show that, even for the real-world Xiamen-Shenzhen railway corridor, the GUROBI solver efficiently generates integrated solutions within acceptable computational times, highlighting the effectiveness of our proposed model.