Optimal pricing and design of station-based bike-sharing systems: A microeconomic model

Abstract

Carefully collected data of nine station-based Bike Sharing Systems (BSS) observed during several years, feed the theoretical formulation of three (aggregated) strategic models representing BSS operation from which the optimal design and pricing is derived. The models include both the operator's costs (investment and operation) and users' costs (time to walk to-from a station, waiting at a station, and time while cycling). The design variables are station spacing, number and capacity of stations, number of bicycles and bike repositioning. Once optimized, the design variables lead to cost functions and optimal pricing. In the first model, a permanent equilibrium without waiting times is assumed. In the second model, waiting at stations (due to a lack of bicycles or docking sites) is introduced in an aggregate form, which results in an increase in the optimal number of bikes and docking sites, making the optimal money price per trip to increase. The third and final model introduces repositioning of bicycles in order to diminish waiting time, making the optimal price grow even further. We obtain an optimal subsidy per trip that grows with the area covered by the BSS, which has implications for its actual implementation in large cities and their spatial and social equity. The optimal pricing scheme is caused by economies of scale due to the reduction in users' access and egress times as the density of stations increases (positive externality) in addition to a fixed operator cost.