Balancing public bicycle sharing system using inventory critical levels in queuing network

Public Bicycle Sharing System has recently been developed and installed in many cities as a workable and popular transportation system. There are still some noticeable challenges associated with the operation of the system, like responding to all renting requests and all demands of vacant docks for returning bikes. Balancing the inventory of stations is necessary to minimize the rejected demands of bikes and the empty lockers. Here, critical levels are defined to control requests of different routes in which a demand of a specified destination is accepted if the inventory of the original station is higher than the route’s critical level. The capacity of stations and the fleet size are determined in addition to the different critical levels considering a constraint for the fleet size of the system. After developing the model using the Jackson network, a genetic algorithm is developed to obtain the proper amounts of variables for balancing the inventory of the system as much as possible. Finally, different examples are worked through to evaluate the applicability of the proposed method.