Stochastic programming model for integrating bus network design and dial-a-ride scheduling

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, mode - demand responsive transit, planning - methods, planning - integration, planning - service level, planning - service improvement, ridership - demand


Public transit, bus, dial-a-ride transportation, vehicle routing, stochastic programming, heuristic


Travel demands in remote areas are scattered and unstable. Thus, the integration of different types of transportation can be beneficial for improving the service level of transportation systems in remote areas. This study proposes a two-stage stochastic programming (SP) model for the integrated planning of a fixed-route–fixed-schedule bus service and dial-a-ride (DAR) transportation (DART) in remote areas. In the first stage, the route and timetable of a bus line are optimized as a set partitioning problem. In the second stage, DART is formulated as a pickup and delivery vehicle routing problem with time windows (PDVRPTW). A hybrid algorithm is developed to solve the two-stage SP problem. Case studies are presented to validate the planning model and the solution algorithm. Results show that the integration of bus and DAR services and the implementation of DART as PDVRPTW considerably reduce unserved demands and improve the service of the entire system.


Permission to publish the abstract has been given by Taylor&Francis, copyright remains with them.