A dynamic programming approach to synchronize train timetables

This article focuses on synchronizing timetables of train services at a rail transfer station. The main aim is to determine an optimal schedule of train services, given that the departure and arrival times of some particular trains are known. An exponential utility function is introduced to measure the synchronization levels between different train services. A nonlinear integer programming model is proposed to achieve the objective of a synchronized timetable. A dynamic programming approach is then designed to solve the developed model. Finally, a numerical example with real-world datasets is implemented to demonstrate the effectiveness of the proposed approaches.