Customized Optimization Method for Trip Pricing and of Bike-Sharing System Design under the Uneven Deployment of Public Transport Stations

Shared bike stocks around public transport (PT) stations are directly affected by the demand of PT. Even existing studies confirm that pricing and design of a bike-sharing system (BSS) further influences the interchange ridership to choose shared bike as intermodal option, but they insufficiently considered the limitation of uneven deployment of PT station. In our study, firstly, we analyze the calculation of two critical parameters: arrival and departure rates of the BSS under the diversity of the deployment of PT stations. Based on these parameters, trip price and bike station density are then introduced as decision variables to maximize the overall benefits objective of BSS, which contains the costs of both operator and users. Secondly, unlike the existing set covering variants, we develop a computational amiable continuous approximation (CA) model to optimize the generalized costs of trip revenue, bike station location, fleet size, dock quantity, and daily reposition. Distinct from other method, CA model with density as a decision variable provides an effective approach to avoid NP-hardness of location optimization problems. By analyzing the structure and properties of this objective function, the innovative proposed closed-form formulation of the two decision variables can be used for improving the efficient computation in large-scale network. Finally, the case studies are applied to validate our proposed models. The result demonstrates that incorporating pricing into BSS planning under multimodal demands of PT can significantly improves the overall benefits of the system and a reduction in user access costs, the economies of scale in BSSs exhibit a complementary relationship with demand distribution.