Frequency-based zonal flexible bus design considering order cancellation

Order cancellation is ubiquitous in on-demand mobility pre-booking systems, which affects the pricing and operational strategies of on-demand mobility services. This paper investigates the order cancellation behaviour in a frequency-based flexible bus (FB) system, which provides customized door-to-door service, considering stochastic elastic demand volume and stochastic spatial demand distribution. A two-stage stochastic model that simultaneously optimises the FB service price, FB dispatching, and passenger assignment is developed while capturing the effect of pre-booked order cancellation probability. This cancellation probability is calculated based on the pricing and availability of street-hailing taxi and FB services. The availability of FBs is derived from the underlying stochastic demand and order assignment process, which makes the model nonlinear. To solve the mixed integer nonlinear model, a two-phase decomposition scheme is employed, and then approximation techniques are implemented to make each decomposed problem solvable by commercial solvers. Finally, a gradient decent solution algorithm is applied. Numerical studies are conducted to show the necessity of capturing the impact of order cancellation and illustrate the influence of cancellation penalty, taxi price, and zone division. Finally, a case study with Chengdu data is implemented to examine the performance of our solution algorithm for large-scale optimisation.