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

• Published in: Transportation research. Part B: methodological 2019-09, Vol.127, p.201-224
• Main Authors: Zhang, J., Meng, M., Wang, David, Z.W.
• Format: Article
• Language: English
• Subjects: Algorithms; Bicycles; Bike relocation/bike repositioning; Dockless bike sharing; Dynamic pricing strategy; Dynamic user equilibrium; Mathematical analysis; Negative price; Prices; Pricing; Pricing policies; Reinforcement; Traffic assignment; Traffic models; Transportation; Transportation models; Travel patterns; Travellers
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2019.07.007

•We introduce a dynamic pricing strategy with negative prices into bike sharing systems.•This is the first study to deal with the bike relocation or bike repositioning problem using user-based approach in dockless bike sharing system.•A dynamic traffic assignment model and its solution algorithm are developed to capture travellers’ mode-path choice behaviour in response to the proposed dynamic pricing strategy.•A systematic comparison among the traditional positive price strategy, free price strategy and the proposed strategy is analysed. 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.