针对乘车需求波动下网约车平台间存在乘车需求竞争和乘运供应竞争的最优定价问题，以平台期望收益最大化为目标，运用最优控制论方法，构建不同竞争情形下的网约车平台动态定价模型，并利用哈密尔顿函数及模型推导，求得最优动态竞争价格解以及乘运供应率与需求率的变化轨迹。结果表明：平台最优动态竞争价格随市场需求的波动而动态变化，且最优价格可以有效调控平台供应能力，促使平台供需匹配，优化平台期望收益。此外，乘车需求市场竞争越激烈，平台最优价格越低，而乘运供应市场竞争越激烈，最优价格越高。平台间竞争的加剧将降低平台的期望收益，且平台期望收益随着固定佣金报酬率的提高先增大后减小。
In recent years, ride-hailing platforms based on the sharing economy have been rapidly popularized and have subverted the traditional taxi market. These platforms often face the mismatch between supply and demand caused by market demand fluctuations and the competition between platforms. In view of the optimal pricing problem with the competitions of demand and supply among ride-hailing platforms under the ride demand fluctuation. Using optimal control theory, the dynamic pricing models considering platform competition with different conditions in which the object is to maximize platform expected profit is constructed. The optimal dynamic competitive price solution is deducted using Hamiltonian function, and the demand rate and supply rate is presented. Through the model analysis and numerical simulation, the optimal dynamic competitive pricing strategy based on time change under different market situations is studied. The influences of supply market competition, demand market competition and fixed commission contract on platform pricing and profit are analyzed. Results show that the optimal dynamic competitive price of the platform changes dynamically with the fluctuation of market demand, and the optimal price can effectively regulate the supply capacity, promote the matching of supply and demand, and optimize the expected revenue of the platform. In addition, the more intense the competition in the ride demand market, the lower the optimal price of the platform, while the more intense the competition in the supply market, the higher the optimal price. The intensified competition between platforms will reduce the platform's expected revenue, and the expected revenue will first increase and then decrease with the increase in the fixed commission rate of return. This study can provide some management insights for ride-hailing platforms' pricing decisions, supply-demand match and competitive strategy.
[1] Cramer J, Krueger A B. Disruptive change in the taxi business:The case of uber[J]. American Economic Review, 2016, 106(5):177-82.
[2] Ma H, Fang F, Parkes D C. Spatio-temporal pricing for ridesharing platforms[R]. Working Paper, Cornell University, 2018.
[3] Yan C W, Zhu H L, Korolko N, et al. Dynamic pricing and matching in ride-hailing platforms. Naval Research Logistics, 2020, 67(8):705-724.
[4] Bimpikis K, Candogan O, Saban D. Spatial pricing in ride-sharing networks[J]. Operations Research, 2019, 67(3):744-769.
[5] Cachon G P, Daniels K, Lobel R. The role of surge pricing on a service platform with self-scheduling capacity[J].Manuf-acturing & Service Operations Management, 2017, 19(3):368-384.
[6] Zha Liteng, Yin Yafeng, Du Yuchuan. Surge pricing and labor supply in the ride-sourcing market[J]. Transportation Research Procedia, 2017, 23:2-21.
[7] Sun L, Teunter R H, Babai M Z, et al. Optimal pricing for ride-sourcing platforms[J]. European Journal of Operational Research, 2019, 278(3):783-795.
[8] Bai J, So K C, Tang C S, et al. Coordinating Supply and Demand on an On-Demand Service Platform with Impatient Customers[J]. Manufacturing & Service Operations Management, 2019, 21(3):497-711.
[9] Hu Ming, Zhou Yun. Price, wage and fixed commission in on-demand matching[R].Working Paper, University of Toronto, 2019.
[10] Taylor T. On-demand service platforms[J]. Manufacturing & Service Operations Management, 2018, 20(4):704-720.
[11] Feng Lin. Dynamic pricing, quality investment, and replenishment model for perishable items[J]. International Transactions in Operational Research, 2019, 26:1558-1575.
[12] Herbon A, Khmelnitsky E. Optimal dynamic pricing and ordering of a perishable product under additive effects of price and time on demand[J]. European Journal of Operational Research, 2017, 260(2):546-556.
[13] Chen Jing, Dong Ming, Rong Ying, et al. Dynamic pricing for deteriorating products with menu cost[J]. Omega, 2018, 75(3):13-26.
[14] Sato K. Price trends and dynamic pricing in perishable product market consisting of superior and inferior firms[J]. European Journal of Operational Research, 2019, 274(1):214-226.
[15] Do C T, Tran N H, Huh E N, et al. Dynamics of service selection and provider pricing game in heterogeneous cloud market[J]. Journal of Network & Computer Applications, 2016, 69:152-165.
[16] Amir A, Ali J, Ali K. Dynamic pricing in social networks:The word-of-mouth effect[J]. Management Science, 2018, 64(2):971-979.
[17] Hu Yusheng, Li Jinlin, Ran Lun. Dynamic pricing for airline revenue management under passenger mental accounting[J]. Mathematical Problems in Engineering, 2015,(3):1-8.
[18] 罗利, 萧柏春. 航空客运平行航班动态定价模型[J]. 中国管理科学, 2012, 20(3):104-111.
[19] 韦才敏, 李忠萍, 范衠. 不同博弈框架下多竞争零售商的双渠道供应链定价决策研究[J]. 运筹与管理, 2018, 147(6):67-78.
[20] 高举红, 滕金辉, 侯丽婷,等. 需求不确定下考虑竞争的闭环供应链定价研究[J]. 系统工程学报, 2017, 32(1):78-87.
[21] 沈焱, 王晓明, 张志英. 考虑市场竞争的电信数据业务质量与定价决策[J]. 系统管理学报, 2019, 28(3):457-466.
[22] Sarat K J, Sarmah S P, Subhash C. Price competition between high and low brand products considering coordination strategy[J]. Computers & Industrial Engineering, 2019, 130(1):500-511.
[23] 林志炳, 张岐山. 零售商的动态定价和服务模型分析[J]. 中国管理科学, 2011,19(6):73-78.
[24] Desiraju R, Moorthy S. Manging a distribution channel under asymmetric information with performance requirements[J]. Management Science, 1997, 43(12):1628-1644.
[25] Jorgensen S, Kort P M. Optimal pricing and inventory policies:Centralized and decentralized decision making[J]. European Journal of Operational Research, 2002, 138(3):578-600.
[26] Liu Weihua, Yan Xiaoyu, Wei Wanying, et al. Pricing decisions for service platform with provider's threshold participating quantity, value-added service and matching ability[J]. Transportation Research Part E:Logistics and Transportation Review, 2019, 122:410-432.
