A station location design problem in a bike-sharing system with both conventional and electric shared bikes considering bike users’ roaming delay costs

Bike-sharing systems (BSSs) have emerged in many cities worldwide. One key issue regarding the strategic design of BSSs is the deployment of bike stations. Innovations in technology have enabled new types of bikes, such as shared e-bikes, to work alongside conventional shared bikes. However, existing studies on bike station location design mainly focus on single bike type, and there is a lack of a theoretical model to determine the optimal bike station locations for a BSS where both conventional shared bikes and e-bikes are considered. This study investigates the station location design problem in a BSS with conventional shared bikes and e-bikes. The design problem is formulated as a bi-level optimization problem. The upper-level problem is to determine the optimal station locations with the objective of maximizing social welfare, and the lower-level problem is a multi-period multi-modal network equilibrium problem with pick-up and drop-off constraints. The upper-level problem is solved using the Genetic Algorithm, while the rolling horizon method is used to decompose the lower-level problem into multiple period-specific subproblems. Each subproblem is solved via a block Gauss-Seidel decomposition approach coupled with the revised simplex method and column generation. Numerical examples are given to demonstrate the properties of the problem, illustrate the performance of the solution algorithm, and offer key insights into the planning of BSSs.