Joint Optimization of Transit Network Design, Timetable, and Passenger Assignment With Exact Transfer Behavior Modeling

This study investigates the problem of joint optimization of transit network design, timetable, and passenger assignment with exact transfer behavior modeling. The problem is formulated as a bi-level mixed-integer bilinear program to capture passengers’ realistic path choice behavior. The upper-level model aims to minimize the weighted sum of the cost of bus route construction, bus route operation, bus station construction, travel time of passengers, the delay caused by failures in aboarding to the bus trips at the origin, the delay caused by failures in transfer between the bus trips, and the overflow delay when the bus trip operates at capacity. The lower-level model aims to minimize the travel time of passengers. The travel time of passengers is formulated as the sum of the waiting time for boarding, the transfer time, and the in-vehicle travel time. The passenger transfer time and the delay caused by failures in transfer between the bus trips are formulated with exact modeling of passenger transfer behavior. This bi-level mixed-integer bilinear program is transformed into an equivalent mixed-integer bilinear program with equilibrium constraints using Karush-Kuhn-Tucker conditions. To seek a solution of good quality to the proposed model while not requiring a large amount of computer memory, a Benders decomposition algorithm integrated with piecewise linearization is developed. A numerical application demonstrates that the proposed model is able to achieve 3.49% lower total cost than the baseline model assuming passenger transfer time to be half of the headway.