A hub location inventory model for bicycle sharing system design: Formulation and solution

This study addresses a strategic design problem for bicycle sharing systems incorporating bicycle stock considerations. The problem is formulated as a hub location inventory model. The key design decisions considered are: the number and locations of bicycle stations in the system, the creation of bicycle lanes between bicycle stations, the selection of paths of users between origins and destinations, and the inventory levels of sharing bicycles to be held at the bicycle stations. The design decisions are made with consideration for both total cost and service levels (measured both by the availability rate for rental requests at the pick-up rental stations and coverage of the origins and destinations). The optimal design of this system requires an integrated view of the travel costs of users, bicycle inventory costs and facility costs of bicycle stations and bicycle lanes as well as service levels. The purpose of this study is to create a formal model that provides such an integrated view, and to develop methods for obtaining solutions for the design variables in practical situations. The complexity of the problem precludes the exact solution of the optimization problem for instances of realistic size, and so we propose a heuristic method for efficiently finding near-optimal solutions. In the test problem for which enumeration is possible, the heuristic solution is within 2% optimal. Finally, a numerical example is created to illustrate the model and proposed solution algorithm. 2011 Elsevier Ltd. All rights reserved.