Optimal extension of rail transit lines

A bilevel model for optimizing the extension of a rail transit line over a planning horizon is presented. In the upper level planning problem, planners make decisions regarding construction and investment in each period with the objective of net present worth maximization. In the lower level operational program, transit operators maximize the social welfare by setting the fare, headway, and vehicle size subject to the train capacity constraint. After the exploration of the model's structure, a tighter reformulated program is proposed and solved as a dynamic program. Numerical studies demonstrate that even without a budget limit phased development can be preferable to a one-time extension.