Cooperative design of feeder bus and bike-sharing systems

Feeder services, which provide travellers effective access from local areas to trunk-line systems, are essential, especially when the long-haul trunk routes are designed with large spacing between stations. Apart from the short-haul bus, the development of bike-sharing systems has led to a powerful supplementary feeder service. Most research on feeder services focuses on the separate design of bike and bus systems, but their joint design deserves further study. This research proposes a bi-level mixed-integer programming model to simultaneously design the locations of feeder buses and shared bike stations as well as the bus routes. A modified genetic algorithm that encapsulates the fixed-point iteration and Frank-Wolfe algorithms is developed to solve the model for large network applications. Numerical examples are given to compare the joint design with the separate design. The key factors that affect the design outcomes are investigated. The effects of joint design on operators and travellers are also discussed.