A robust optimization approach for itinerary planning with deadline

We propose a robust optimization approach to address the itinerary planning problem with deadline in public transit networks. Given departure times at origins and deadlines at destinations, we help the travelers meet the deadlines as much as possible. Our model maximizes the size of the uncertainty set of arc travel times, while guaranteeing that the corresponding worst-case arrival time of itinerary would not exceed the deadline. We exploit the model's structure and develop efficient solution algorithms. We demonstrate in numerical studies that our approach can effectively mitigate the lateness and can solve real-world instances within one second.