Robust transit network design with stochastic demand considering development density

This paper analyzes the influence of unban density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail or bus, and flexible services, such as dial-a-ride or taxi. Rapid transit services are operated on fixed routes and fixed schedules which may include multiple lines, whereas dial-a-ride services are made available to carry the demand realized on a particular time that exceeds the capacity of rapid transit services. A robust formulation is proposed to address the stochastic demand as captured in a polyhedral uncertainty set. It is reformulated as a mixed integer linear program by replacing the related uncertainty constraints by its dual problem. An example is provided to illustrate the performance of this formulation.