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A dynamic pricing scheme with negative prices in dockless bike sharing systems

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  • Zhang, J.
  • Meng, M.
  • Wang, David, Z.W.

Abstract

To achieve bike relocation11The bike relocation mentioned in this paper is also referred as bike repositioning in the literature. through travellers’ spontaneous behaviour in dockless bike sharing systems, an innovative dynamic pricing scheme with negative prices is introduced. In normal situation, users pay a positive price to operators for using a bike. However, when imbalanced distribution of bikes occurs in the system, users who cycle from the oversupplied area to undersupplied area will receive monetary reward from the operator, i.e., negative pricing applies. A user equilibrium dynamic traffic assignment model is developed to capture travellers’ mode-path choice behaviour in response to the proposed dynamic pricing strategy. Travellers can either use a single transportation mode (e.g. walking, cycling and bus) or take multiple modes to complete their trips. The user equilibrium travel pattern is formulated as a variational inequality problem and then solved by a path-flow swapping algorithm. Two numerical examples are conducted to demonstrate that the proposed dynamic pricing strategy with negative prices is effective in terms of attracting users as well as achieving a more balanced bike repositioning, especially when the number of bikes provided in the system is limited.

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  • Zhang, J. & Meng, M. & Wang, David, Z.W., 2019. "A dynamic pricing scheme with negative prices in dockless bike sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 201-224.
    • Handle: RePEc:eee:transb:v:127:y:2019:i:c:p:201-224
    DOI: 10.1016/j.trb.2019.07.007
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    1. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    2. Szeto, W.Y. & Shui, C.S., 2018. "Exact loading and unloading strategies for the static multi-vehicle bike repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 176-211.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Long, Jiancheng & Szeto, W.Y. & Du, Jie & Wong, R.C.P., 2017. "A dynamic taxi traffic assignment model: A two-level continuum transportation system approach," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 222-254.
    5. Wang, David Z.W. & Du, Bo, 2016. "Continuum modelling of spatial and dynamic equilibrium in a travel corridor with heterogeneous commuters—A partial differential complementarity system approach," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 1-18.
    6. Xu, Min & Meng, Qiang & Liu, Zhiyuan, 2018. "Electric vehicle fleet size and trip pricing for one-way carsharing services considering vehicle relocation and personnel assignment," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 60-82.
    7. Francesco Ciari & Milos Balac & Michael Balmer, 2015. "Modelling the effect of different pricing schemes on free-floating carsharing travel demand: a test case for Zurich, Switzerland," Transportation, Springer, vol. 42(3), pages 413-433, May.
    8. D. Zhang & A. Nagurney, 1997. "Formulation, Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 417-444, May.
    9. Qian, Xinwu & Zhang, Wenbo & Ukkusuri, Satish V. & Yang, Chao, 2017. "Optimal assignment and incentive design in the taxi group ride problem," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 208-226.
    10. Lo, Hong K. & Szeto, W. Y., 2004. "Modeling advanced traveler information services: static versus dynamic paradigms," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 495-515, July.
    11. Regue, Robert & Recker, Will, 2014. "Proactive vehicle routing with inferred demand to solve the bikesharing rebalancing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 192-209.
    12. Nicolosi, Marco, 2010. "Wind power integration and power system flexibility-An empirical analysis of extreme events in Germany under the new negative price regime," Energy Policy, Elsevier, vol. 38(11), pages 7257-7268, November.
    13. Anna Nagurney & Ding Zhang, 1997. "Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria," Transportation Science, INFORMS, vol. 31(2), pages 147-158, May.
    14. Zheng, Nan & Waraich, Rashid A. & Axhausen, Kay W. & Geroliminis, Nikolas, 2012. "A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1291-1303.
    15. Ho, Sin C. & Szeto, W.Y., 2017. "A hybrid large neighborhood search for the static multi-vehicle bike-repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 340-363.
    16. Dell'Amico, Mauro & Hadjicostantinou, Eleni & Iori, Manuel & Novellani, Stefano, 2014. "The bike sharing rebalancing problem: Mathematical formulations and benchmark instances," Omega, Elsevier, vol. 45(C), pages 7-19.
    17. Schuijbroek, J. & Hampshire, R.C. & van Hoeve, W.-J., 2017. "Inventory rebalancing and vehicle routing in bike sharing systems," European Journal of Operational Research, Elsevier, vol. 257(3), pages 992-1004.
    18. Erdoğan, Güneş & Battarra, Maria & Wolfler Calvo, Roberto, 2015. "An exact algorithm for the static rebalancing problem arising in bicycle sharing systems," European Journal of Operational Research, Elsevier, vol. 245(3), pages 667-679.
    19. Liu, Wei & Geroliminis, Nikolas, 2017. "Doubly dynamics for multi-modal networks with park-and-ride and adaptive pricing," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 162-179.
    20. Brandstätt, Christine & Brunekreeft, Gert & Jahnke, Katy, 2011. "How to deal with negative power price spikes?--Flexible voluntary curtailment agreements for large-scale integration of wind," Energy Policy, Elsevier, vol. 39(6), pages 3732-3740, June.
    21. Brian D. Wright & Jeffrey C. Williams, 2000. "A theory of negative prices for storage," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 20(1), pages 59-71, January.
    22. Li, Qing & Liao, Feixiong & Timmermans, Harry J.P. & Huang, Haijun & Zhou, Jing, 2018. "Incorporating free-floating car-sharing into an activity-based dynamic user equilibrium model: A demand-side model," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 102-123.
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    7. Li, Chunzhi & Xiao, Wei & Zhang, Dayong & Ji, Qiang, 2021. "Low-carbon transformation of cities: Understanding the demand for dockless bike sharing in China," Energy Policy, Elsevier, vol. 159(C).
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    10. Zakharenko, Roman, 2023. "Pricing shared vehicles," Economics of Transportation, Elsevier, vol. 33(C).
    11. Zhang, Jie & Meng, Meng & Wong, Yiik Diew & Ieromonachou, Petros & Wang, David Z.W., 2021. "A data-driven dynamic repositioning model in bicycle-sharing systems," International Journal of Production Economics, Elsevier, vol. 231(C).
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    14. Jun Tu & Juan Du & Min Huang, 2023. "Competition between Green and Non-Green Travel Companies: The Role of Governmental Subsidies in Green Travel," Sustainability, MDPI, vol. 15(9), pages 1-33, May.
    15. Liu, Yixiao & Tian, Zihao & Pan, Baoran & Zhang, Wenbin & Liu, Yunqi & Tian, Lixin, 2022. "A hybrid big-data-based and tolerance-based method to estimate environmental benefits of electric bike sharing," Applied Energy, Elsevier, vol. 315(C).
    16. Zhang, Si & Sun, Huijun & Wang, Xu & Lv, Ying & Wu, Jianjun, 2022. "Optimization of personalized price discounting scheme for one-way station-based carsharing systems," European Journal of Operational Research, Elsevier, vol. 303(1), pages 220-238.
    17. Zhou, Yaoming & Lin, Zeyu & Guan, Rui & Sheu, Jiuh-Biing, 2023. "Dynamic battery swapping and rebalancing strategies for e-bike sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    18. Dongdong Feng & Lin Cheng & Mingyang Du, 2020. "Exploring the Impact of Dockless Bikeshare on Docked Bikeshare—A Case Study in London," Sustainability, MDPI, vol. 12(15), pages 1-18, July.
    19. Zhuang, Zheng-Yun & Chung, Cheng-Kung, 2024. "Dissecting the visiting willingness of driving visitors facing a retail market's dual-pricing policy for parking," Journal of Retailing and Consumer Services, Elsevier, vol. 78(C).
    20. Gu, Wei & Yu, Xiaoru & Zhang, Shichen & Yan, Xiangbin & Wang, Chen, 2023. "To outsource or not: Bike-share rebalancing strategies under the service quality deviation of a third party," European Journal of Operational Research, Elsevier, vol. 310(2), pages 847-859.
    21. Meijian Yang & Enjun Xia, 2021. "A Systematic Literature Review on Pricing Strategies in the Sharing Economy," Sustainability, MDPI, vol. 13(17), pages 1-28, August.
    22. Zijia Wang & Lei Cheng & Yongxing Li & Zhiqiang Li, 2020. "Spatiotemporal Characteristics of Bike-Sharing Usage around Rail Transit Stations: Evidence from Beijing, China," Sustainability, MDPI, vol. 12(4), pages 1-19, February.

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