Optimal pricing of customized bus services and ride-sharing based on a competitive game model

Customized bus services and ride-sharing are two emerging online-hailing transport modes that greatly improve public transport efficiency and convenience, especially for night services. In this study we consider the optimal pricing problem for a platform providing these two service modes. Ride-sharing vehicles can be either driver- or platform-owned. We formulate a competitive game model in which the objective is to maximize the profits of each mode based on passengers' transport mode choice, which is strongly affected by utility functions based on the passengers' subjective value of time and the price of the transport mode. We develop a questionnaire to measure passengers' subjective value of time and use the results to determine the relevant parameter value in the model. We then conduct a sensitivity analysis to study the effects of different parameters on the optimal prices and profits. The profits earned by both customized bus services and ride-sharing are positively correlated with the proportion of platform-owned vehicles. Furthermore, we conduct a series of simulation experiments to verify the validity of the numerical results. The results indicate that the absolute difference ratios between the simulation and numerical results are less than 1% when the number of passengers is set to over 8000. (C) 2021 Elsevier Ltd. All rights reserved.