An optimized two-phase demand-responsive transit scheduling model considering dynamic demand

Demand-responsive transit has gradually attracted attention in recent years for its flexibility, efficiency, and ability to meet the diverse travel demands of passengers. To improve the operational efficiency of demand-responsive transit (DRT) with dynamic demand, this study innovatively investigates the DRT scheduling problem from multiple perspectives, such as multi-vehicle, non-fixed stop, and dynamic demand, and constructs a two-phase DRT vehicle scheduling model. In the first phase, a static scheduling model is established with the objective of minimizing vehicle setup cost, operation cost, and CO₂ emission cost according to passenger travel satisfaction. In the second phase, a dynamic scheduling model is constructed with the objective of minimizing the increased vehicle operation cost in response to dynamic demand and the penalty cost of violating the time window and rejecting passengers. In addition, in the first static phase, an improved heuristic algorithm is used to obtain optimal routes based on passengers’ subscriptions, while in the second phase, an insertion algorithm is designed to solve the dynamic scheduling model based on the previous schedule. Finally, cases are applied to a realistic network in Chaoyang District, Beijing, China, to verify the effectiveness of the proposed scheduling model. The results demonstrate that dynamic scheduling can enable more passengers to be served with a slight increase in total vehicle operating costs. Besides, the introduction of the non-fixed stop service model can significantly reduce total travel time by up to 8.8% compared with the fixed stop service. The proposed models and solution algorithms in this study are practical for real-world applications.