The Static Rebalancing Problem in Bicycle-Sharing Systems with Unusable Bicycles

This paper addresses the static bicycle rebalancing problem with multiple vehicles and multiple visits. The objective is to rebalance the stations of a bicycle-sharing system to reach the target number of good bicycles minimizing the total travelling time using a fleet of homogeneous vehicles. The vehicles have identical capacities and service time limits, and are allowed to visit the stations multiple times. One major challenge is that the unusable bicycles and the maintenance operations of bicycles are considered. In this paper, we propose a mixed integer programming model for solving the problem. The repair station is introduced to the model and all unusable bicycles at stations are delivered to the repair station. Considering the possibility of being outsourced to a third-party service company, our study requires that all vehicles depart from and return to the depot with no bicycles.The mathematical formulation of the problem is computationally tested.