Joint design of shared-bike and transit services in corridors

The prevalence of shared bikes in many cities is a double-edged sword to the local mass transit services. Some transit patrons may switch to cycling, causing declines in the transit ridership. Others may benefit from using bikes instead of walking to access transit. The complicated interactions between the two modes entail the necessity of designing them jointly. Unfortunately, the literature has focused on either the design of a single mode or joint designs idealized by assuming a uniform demand pattern. The latter class of works has limited practical values. This paper develops a continuum approximation (CA) model for optimizing the hybrid design of shared-bike and transit services in a corridor under spatially heterogeneous demand patterns. The model minimizes the generalized system cost considering various route options that patrons can choose from, including transit routes with walking or biking access and bike-only routes. The methodological challenges that arise due to patrons’ route choices in the heterogeneous operating environment are overcome by incorporating a route assignment model into the CA modeling framework. We propose a bi-level algorithm to solve the model, where the upper level optimizes the hybrid design by exploiting some analytical properties of the CA model, and the lower level calculates the route assignment equilibrium. Numerical experiments show that the optimal hybrid design outperforms the conventional transit design for a wide range of operating conditions. The cost saving can be over 20%. Under certain conditions, the hybrid design can even reduce the total operating cost, making bike-sharing profitable for transit agencies. The practical applicability of our model is demonstrated via a case study of a real bus line in Chengdu, China