Two-stage model for flex-route transit scheduling

A two-stage scheduling model is designed for the flex-route transit to deal with predetermined requests and real-time requests. An optimal model for the vehicle routing problem, which minimizes passenger travel costs and vehicle operating costs, is built as the first-stage scheduling model to serve predetermined requests. The simulated annealing algorithm is developed to solve the first-stage model and an initial vehicle routing plan can be obtained. The second-stage scheduling model is established for real-time requests, and four types of passengers are arranged into the vehicle routing plan through the heuristic insertion algorithm. The simulation experiments based on a realistic case demonstrate the feasibility of this two-stage scheduling model, and the results indicate that there would be a better system performance if more passengers choose to make appointments for flex-route service. There is approximately a 10% improvement in system performance when demand reaches 25 passenger/h and 70% of passengers make appointments, compared with the scenario under pure real-time passenger demand.