A time-space network flow approach to dynamic repositioning in bicycle sharing systems

• Published in: Transportation research. Part B: methodological Vol. 103; pp. 188 - 207
• Main Authors: Zhang, Dong, Yu, Chuhang, Desai, Jitamitra, Lau, H.Y.K., Srivathsan, Sandeep
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-09-2017; Elsevier Science Ltd
• Subjects: Algorithms; Arrivals; Bicycle sharing systems; Bicycles; Computer applications; Convexification and linearization; Demand forecasting; Dynamic repositioning; Forecasting; Heuristic; Heuristic algorithm; Heuristic methods; Metropolitan areas; Optimization; Peak periods; Population density; Population growth; Repositioning; Resource utilization; Route planning; Routing; Subways; Time-space network flow model; Traffic congestion; Transportation; Urban transportation; Vehicle routing; Bicycle sharing systems; Dynamic repositioning; Convexification and linearization; Heuristic algorithm; Time-space network flow model; Demand forecasting
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2016.12.006

•An integrated model is proposed to simultaneously consider the user dissatisfaction forecasting, bicycle repositioning and vehicle routing.•An efficient linearization method is proposed to transfer the non-linear model into an equivalent linear model.•A math-heuristic algorithm is proposed.
Faced with increasing population density, rising traffic congestion, and the resulting upsurge in carbon emissions, several urban metropolitan areas have instituted public bicycle sharing system as a viable alternative mode of transportation to complement existing long-distance bus- and metro- transit systems. A pressing issue that needs to be addressed in bike sharing systems is the accrued imbalance of bicycles between commuter demands and inventory levels at stations. To overcome this issue, a commonly employed strategy is to reposition bicycles during off-peak periods (typically at night) when no new user arrivals are expected. However, when such an imbalance occurs during day-time peak hours, such a passive strategy would result in lower resource utilization rates. To overcome this drawback, in this study, we propose a dynamic bicycle repositioning methodology that considers inventory level forecasting, user arrivals forecasting, bicycle repositioning, and vehicle routing in a unified manner. A multi-commodity time-space network flow model is presented, which results in an underlying complex nonlinear optimization problem. This problem is then reformulated into an equivalent mixed-integer problem using a model transformation approach and a novel heuristic algorithm is proposed to efficiently solve this model. Specifically, the first stage involves solving the linear relaxation of the MIP model, and a set covering problem is subsequently solved in the second stage to assign routes to the repositioning vehicles. The proposed methodology is evaluated using standard test-bed instances from the literature, and our numerical results reveal that the heuristic algorithm can achieve a significant reduction in rejected user requests when compared to existing methods, while yet expending only minimal computational effort.