Optimal service zone and headways for flexible-route bus services for multiple periods

Where private ridesharing companies such as Uber and Lyft are transforming the transit sector by making flexible transit cheaper and more readily available than ever before, it may be beneficial for public transportation agencies to adapt to the changing marketplace and provide flexible bus services in low to mid-demand density areas such as suburban or rural areas. This paper proposes an optimization model in which the service area for the flexible bus operations is jointly optimized with headways with time-dependent demand densities. The closed-form solution that minimizes the average costs of user and operator is obtained with analytic optimization. The model presented in this paper may be a helpful planning resource to determine the feasibility of flexible bus services where fixed-route transit operation is not desirable due to the lack of ridership, especially in suburban and rural regions. Numerical case studies and sensitivity analyses for critical operation factors are presented.