Static green repositioning in bike sharing systems with broken bikes

This study aims to propose a methodology to reposition both good and broken bikes in a bike-sharing network in order to achieve a perfect balance between bike demand and supply at each station and make sure that all broken bikes are moved back to the depot. The objective of this repositioning operation is to minimize the total CO2 emissions of all repositioning vehicles. A Mixed Integer Linear Program (MILP) model is presented to formulate the problem mentioned above and a commercial solver is used to solve it for small applications. Using example applications, problem characteristics and the factors that affect the CO2 emissions are discussed. The results indicate that allowing multiple visits can reduce vehicle emissions. Moreover, when the percentage of broken bikes in the system increases, the CO2 emissions increase. Furthermore, if there is a tolerance for meeting the demand target, when this tolerance increases, the CO2 emissions decrease. In addition, when the distance of a link in an optimal route increases, the resultant emissions may remain unchanged. Besides, when the vehicle capacity increases, the CO2 emissions decrease. The real world instances of Citybike Vienna are used to compare emission and distance minimization solutions and investigate the runtime complexity of the proposed model. The results demonstrate that a shorter distance may not necessarily lead to lower emissions. The results also show that as the number of vehicles increases, the total emissions and runtime increase. A clustering method based on the nearest neighbor heuristic together with a commercial solver is used to solve a large real-world instance. This result confirms the possibility of using the clustering approach to reduce the running time for large network instances with multiple vehicles.