Two-phase optimization model for ride-sharing with transfers in short-notice evacuations

Optimization of on-demand transportation provisions and ride-sharing services in evacuations may provide increased network capacity and enhanced evacuation performance to transportation systems and improve equity and disaster preparedness for community and society. This paper proposes a two-phase model for optimizing trip planning and operations by integrating a ride-sharing process in short-notice evacuations, to allow a joint optimization of driver-rider matching and necessary transfer connections among shared vehicle trips. In the first phase, following network topology information and personal requests, a vehicle-space-time hyper dimensional network is developed by constructing vehicle-space-time vertexes and arcs. In the second phase, based on the constructed vehicle-space-time network, a new time-discretized multi-rider multi-driver network flow model is built to formulate ride-sharing with connecting transfers. A Lagrangian relaxation solution approach is designed to solve the model in a real-world network scenario. Numerical analyses are conducted with considerations given to the three operating parameters (detour tolerance of driver, penalty factor for transfer time, and maximum allowable parking time) in the method, and the analysis results show that the proposed model can not only meet the evacuation trip needs of the participating parties but it also supports personalized requests and on-demand accesses. A small sample network is used to theoretically test the whole model and the underlying concepts and solution strategy to show each step implemented in details, and finally the applicability of the method is demonstrated using the Chicago City network.