Transit network design under demand uncertainty

This paper develops a service reliability based formulation for the transit network design problem 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. We utilize the notion of service reliability to address the issue of demand uncertainty and formulate the problem as a two-phase stochastic program in which the configuration of the transit network and frequencies of the routes are determined in phase-1 while the dial-a-ride services are determined in phase-2 depending on the demand realization. The objective is to decide the optimal combination of these two service types in order to minimize the total expected operating cost while serving all OD demands. A gradient solution approach is utilized to solve the problem. An illustrative example demonstrates the formulation and the procedure.