Optimal Deployment of Electric Bicycle Sharing Stations: Model Formulation and Solution Technique

This paper studies the problem of deploying electric bicycle (e-bike) sharing stations and determining their capacities, i.e. the number of shared e-bikes and charging piles, considering travelers’ responses to the charging demands and different deployment schemes. Given a one-way station-based setting, we propose an e-bike sharing network where the generalized trip cost is measured as the sum of the delay cost at stations and the travel time en-route. To estimate the trip costs, we modeled the pick-up and drop-off e-bikes at each sharing station as two different queues affected by e-bikes’ charging demands, and described the traffic flow of shared e-bike on each route based on Greenshield’s model. Further, the e-bike sharing station deployment problem was then formulated as a bi-level programming model, taking into account the government’s and individual travelers’ profits. The uniqueness of solution was proved. For the purpose of solution approach, this bi-level model was then reformulated into a single-level mixed-integer programming model, and a hybrid particle swarm optimization algorithm was proposed to solve the single-level model. Numerical experiments were presented to demonstrate the validity of the proposed model and solution technique. More importantly, through numerical experiments, further insights for designing an e-bike sharing system were examined and discussed: 1) sharing stations are bottlenecks in the e-bike sharing network, since the charging activities cause travelers large delay costs; 2) a well-designed quick-charging technology and reservation policy could be incorporated into e-bike sharing systems to reduce system costs; 3) the proposed hybrid particle swarm optimization algorithm shows good solution quality and convergence performance.