Robust Multi-period Fleet Allocation Models for Bike-Sharing Systems

This paper presents mathematical programming models that generate optimal daily allocation of bicycles to the stations of a bike-sharing system. First, a time-space network is constructed to describe time-dependent bike flows in the system. Next, a bike fleet allocation model that considers average historical demand and fixed fleet size is established based on the time-space network. In addition to fleet allocation in multiple periods, this model generates least cost empty bicycle redistribution plans to meet demand in subsequent time periods. The model aims to correct demand asymmetry in bike-sharing systems, where flow from one station to another is seldom equal to the flow in the opposing direction. An extension of the model that relaxes the fleet size constraint to determine optimal fleet size in supporting planning stage decisions is also presented in the paper. Moreover, we describe uncertain bike demands using some prescribed uncertainty sets and develop robust bike fleet allocation models that minimize total system cost in the worst-case or maximum demand scenarios derived from the uncertainty sets. Numerical experiments were conducted based on the New Taipei City’s public bike system to demonstrate the applicability and performance of the proposed models. In addition, this research considers two performance measures, robust price and hedge value, in order to investigate the tradeoff between robustness and optimality, as well as the benefit of applying robust solutions relative to nominal optimal solutions in uncertain demand situations.