Robust dynamic pricing for bike sharing systems under willingness to pay uncertainty

Bike sharing systems are now an important part of city transport. Their pricing affects revenue, user access, and demand across busy and quiet periods. Many operators still use flat prices, although users may have different willingness to pay by time, trip type, and user group. This study aims to design a pricing model that captures this variation and also protects operators from errors in willingness to pay estimates. A robust linear programming model is developed and tested using 4,505,245 cleaned trips from the 2025 Capital Bikeshare dataset. The model builds willingness to pay uncertainty sets from revealed preference fares for different user segments and time periods. It is tested on a network of 20 origin-destination pairs, six time periods, and three user segments. The proposed model increases annual revenue by 13.5% on average compared with the flat rate baseline. Under reasonable elasticity settings, the revenue gain ranges from 11.8% to 15.2%. Revenue also remains stable under moderate uncertainty and stays higher than the flat rate baseline when robustness levels increase. The equity constrained version shows that access requirements can be maintained while still gaining revenue from dynamic pricing. These findings show that robust dynamic pricing can improve bike sharing revenue without ignoring affordability. The study also provides an empirical price of robustness curve for a real shared mobility network.