Coordinating last-train timetabling with app-based ride-hailing service under uncertainty

Since urban rail transit (URT) service is normally not running on 24 -hour operation in most cities, last -train timetabling is a prominent problem and challenges URT managers constantly. The rise of app -based ride -hailing (ARH) service opens up new opportunities and challenges for last -train operators to better serve late -night passengers. Specifically, when passengers cannot reach their destinations only through URT services during the last -train operation period, passengers could make good use of feasible train -to -train transfers to reach stations closer to their destinations, and transfer to flexible ARH services to reach their final destinations. However, uncertain road conditions and varying passenger travel preferences complicate the coordination of URT services with ARH services. By considering different passengers' traveling preferences, various travel path choices, and uncertain ARH travel times, we formulate a two -stage mixed -integer stochastic optimization model to achieve an optimal last -train timetable design for getting more passengers to their destinations in a cost-effective and efficient way. In addition, we propose a genetic algorithm -based solution strategy which outperforms commercial solvers with its computational performance and has its practicability assured. Through our numerical experiments, we reveal insights about how different customers' preferences and cost components affect the optimal results and provide operational suggestions accordingly for achieving better timetable performance.