考虑客票折扣销售的高铁票额分配
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摘要
为了改善高铁收益,采用折扣销售策略建立多级票价体系.利用随机非线性规划方法,考虑旅客选择行为,构建多级票价多列车多停站网络的票额分配模型,并根据离散时间需求的特点,将其转化为等价的线性规划模型,然后采用CPLEX软件快速求解.按照实际运营的数据规模进行算例分析,求解最优票额分配方案,并分析不同参数下期望总收益的变化规律.结果表明:所提票额分配模型能够优先满足全价和长途需求,计算复杂度满足应用要求;需求强度越低,需求价格弹性越高,差异化服务敏感度越高,折扣销售的期望总收益增加越大;合理设置折扣票价等级可获得最佳期望总收益.实际运营中,应针对具体市场的需求特征利用此模型进行分析测试,为折扣销售和票额分配提供有效依据.
To improve the revenue of high-speed railway, the multi-class fare system was formulated by selling discount tickets. Considering the passengers' choice behaviors, the probabilistic nonlinear programming was used to establish a stochastic ticket allocation model for multi-class fare, multi train and multi-stop station network. According to the characteristics of discrete-time demands, this model was transformed into an equivalent linear programming model solved by CPLEX quickly. The numerical experiments with the actual operation data scale were carried out to obtain the optimal ticket allocation scheme and the change law of the expected total revenue with different parameters was analyzed. The results show that the ticket allocation model gives priority to the demands for full-price and long-distance, and the computational complexity can meet the needs of application. The decrease of the intensity of demand can lead the increase of the price elasticity of demand, the sensitivity of differentiated services, and the increment of the expected total revenue of discount sales. Reasonable fare grade can achieve the best expected total revenue. In actual operation, according to the specific market demand characteristics, analysis and tests of this model should be carried out to provide an effective basis for discount sales and ticket allocation.
To improve the revenue of high-speed railway, the multi-class fare system was formulated by selling discount tickets. Considering the passengers' choice behaviors, the probabilistic nonlinear programming was used to establish a stochastic ticket allocation model for multi-class fare, multi train and multi-stop station network. According to the characteristics of discrete-time demands, this model was transformed into an equivalent linear programming model solved by CPLEX quickly. The numerical experiments with the actual operation data scale were carried out to obtain the optimal ticket allocation scheme and the change law of the expected total revenue with different parameters was analyzed. The results show that the ticket allocation model gives priority to the demands for full-price and long-distance, and the computational complexity can meet the needs of application. The decrease of the intensity of demand can lead the increase of the price elasticity of demand, the sensitivity of differentiated services, and the increment of the expected total revenue of discount sales. Reasonable fare grade can achieve the best expected total revenue. In actual operation, according to the specific market demand characteristics, analysis and tests of this model should be carried out to provide an effective basis for discount sales and ticket allocation.
引文
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[8] 骆泳吉, 刘军, 赖晴鹰,等. 考虑通售席位的旅客列车票额优化方法[J]. 铁道学报, 2016, 38(5): 11-15. DOI:10.3969/j.issn.1001-8360.2016.05.002.Luo Y J, Liu J, Lai Q Y, et al. Optimization of seat inventory allocation for passenger trains with first-come-first-serve seats[J]. Journal of the China Railway Society, 2016, 38(5): 11-15. DOI:10.3969/j.issn.1001-8360.2016.05.002.(in Chinese)
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[13] 刘帆洨, 彭其渊, 梁宏斌, 等. 铁路客运票额预售控制决策模型研究[J]. 铁道学报, 2018, 40(1): 17-23. DOI:10.3969/j.issn.1001-8360.2018.01.03.Liu F X, Peng Q Y, Liang H B, et al. Control and decision model for railway passenger ticket pre-sale[J]. Journal of the China Railway Society, 2018, 40(1): 17-23. DOI:10.3969/j.issn.1001-8360.2018.01.03.(in Chinese)
[14] 史峰, 陈彦, 周文梁, 等. 基于用户平衡分析的铁路旅客列车票额分配计划制定及评价方法[J]. 中国铁道科学, 2008, 29(6): 98-103. DOI:10.3321/j.issn:1001-4632.2008.06.019.Shi F, Chen Y, Zhou W L, et al. Railway passenger train seats allotment plan establishment and evaluation method based on user equilibrium analysis[J]. China Railway Science, 2008, 29(6): 98-103. DOI:10.3321/j.issn:1001-4632.2008.06.019.(in Chinese)
[15] 钱丙益, 帅斌, 陈崇双, 等. 基于旅客buy-up行为的铁路客运专线收益管理模型[J]. 铁道学报, 2013, 35(8): 10-15. DOI:10.3969/j.issn.1001-8360.2013.08.002.Qian B Y, Shuai B, Chen C S, et al. Revenue management model for dedicated passenger line based on passengers' buy-up behavior[J]. Journal of the China Railway Society, 2013, 35(8): 10-15. DOI:10.3969/j.issn.1001-8360.2013.08.002.(in Chinese)
[16] 张力, 蓝伯雄. 基于旅客选择的高速铁路客运收益管理研究[J]. 运筹与管理, 2012, 21(2): 116-125. DOI:10.3969/j.issn.1007-3221.2012.02.018.Zhang L, Lan B X. Revenue management model for high-speed railway based on traveler choice[J]. Operations Research and Management Science, 2012, 21(2): 116-125. DOI:10.3969/j.issn.1007-3221.2012.02.018.(in Chinese)
[17] Hetrakul P, Cirillo C. Accommodating taste heterogeneity in railway passenger choice models based on internet booking data[J]. Journal of Choice Modelling, 2013, 6: 1-16. DOI:10.1016/j.jocm.2013.04.003.
[18] Hetrakul P, Cirillo C. A latent class choice based model system for railway optimal pricing and seat allocation[J]. Transportation Research Part E: Logistics and Transportation Review, 2014, 61: 68-83. DOI:10.1016/j.tre.2013.10.005.
[19] 赵鹏, 李云峰, 李博,等. 基于时段偏好的高铁旅客车次选择行为研究[J]. 北京交通大学学报, 2017, 41(6): 49-54. DOI:10.11860/j.issn.1673-0291.2017.06.008.Zhao P, Li Y F, Li B, et al. Study on the train choice behavior for high-speed railway passengers considering the departure time preference[J]. Journal of Beijing Jiaotong University, 2017, 41(6): 49-54. DOI:10.11860/j.issn.1673-0291.2017.06.008.(in Chinese)
[20] Wang X C, Wang H, Zhang X N. Stochastic seat allocation models for passenger rail transportation under customer choice[J].Transportation Research Part E: Logistics and Transportation Review, 2016, 96: 95-112. DOI:10.1016/j.tre.2016.10.003.
[21] 赵翔, 赵鹏, 姚向明, 等. 高速列车折扣票价与票额分配组合优化模型[J]. 东南大学学报(自然科学版), 2018, 48(4): 759-765. DOI:10.3969/j.issn.1001-0505.2018.04.024.Zhao X, Zhao P, Yao X M, et al. An integrated optimization model of discount fare and ticket allocation for high-speed train[J]. Journal of Southeast University(Natural Science Edition), 2018, 48(4): 759-765. DOI:10.3969/j.issn.1001-0505.2018.04.024.(in Chinese)
[2] Zheng J Z, Liu J, Clarke D B. Ticket fare optimization for China's high-speed railway based on passenger choice behavior[J].Discrete Dynamics in Nature and Society, 2017, 2017: 1-6. DOI:10.1155/2017/6237642.
[3] You P S. An efficient computational approach for railway booking problems[J].European Journal of Operational Research, 2008, 185(2): 811-824. DOI:10.1016/j.ejor.2006.12.049.
[4] Strauss A K, Klein R, Steinhardt C. A review of choice-based revenue management: Theory and methods[J].European Journal of Operational Research, 2018, 271(2): 375-387. DOI:10.1016/j.ejor.2018.01.011.
[5] Hosseinalifam M, Marcotte P, Savard G. Network capacity control under a nonparametric demand choice model[J]. Operations Research Letters, 2015, 43(5): 461-466. DOI:10.1016/j.orl.2015.06.012.
[6] Hosseinalifam M, Marcotte P, Savard G. A new bid price approach to dynamic resource allocation in network revenue management[J]. European Journal of Operational Research, 2016, 255(1): 142-150. DOI:10.1016/j.ejor.2016.04.057.
[7] Ciancimino A, Inzerillo G, Lucidi S, et al. A mathematical programming approach for the solution of the railway yield management problem[J]. Transportation Science, 1999, 33(2): 168-181. DOI:10.1287/trsc.33.2.168.
[8] 骆泳吉, 刘军, 赖晴鹰,等. 考虑通售席位的旅客列车票额优化方法[J]. 铁道学报, 2016, 38(5): 11-15. DOI:10.3969/j.issn.1001-8360.2016.05.002.Luo Y J, Liu J, Lai Q Y, et al. Optimization of seat inventory allocation for passenger trains with first-come-first-serve seats[J]. Journal of the China Railway Society, 2016, 38(5): 11-15. DOI:10.3969/j.issn.1001-8360.2016.05.002.(in Chinese)
[9] 赵翔, 赵鹏, 李博,等. 多列车多停站方案条件下高速铁路票额分配研究[J]. 铁道学报, 2016, 38(11): 9-15. DOI:10.3969/j.issn.1001-8360.2016.11.002.Zhao X, Zhao P, Li B, et al. Study on high-speed railway ticket allocation under conditions of multiple trains and multiple train stop plans[J]. Journal of the China Railway Society, 2016, 38(11): 9-15. DOI:10.3969/j.issn.1001-8360.2016.11.002.(in Chinese)
[10] 宋文波, 赵鹏, 李博, 等. 考虑旅客旅行时间的高速铁路票额分配[J]. 东南大学学报(自然科学版), 2017, 47(5): 1062-1068. DOI:10.3969/j.issn.1001-0505.2017.05.035.Song W B, Zhao P, Li B, et al. High-speed railway ticket allocation considering passenger travel time[J]. Journal of Southeast University(Natural Science Edition), 2017, 47(5): 1062-1068. DOI:10.3969/j.issn.1001-0505.2017.05.035.(in Chinese)
[11] 骆泳吉. 铁路席位控制建模与优化方法研究[D]. 北京: 北京交通大学, 2017.Luo Y J. Modeling and optimization of seat inventory control for passenger railway[D]. Beijing: Beijing Jiaotong University, 2017.(in Chinese)
[12] Jiang X S, Chen X Q, Zhang L, et al. Dynamic demand forecasting and ticket assignment for high-speed rail revenue management in China[J].Transportation Research Record: Journal of the Transportation Research Board, 2015, 2475(1): 37-45. DOI:10.3141/2475-05.
[13] 刘帆洨, 彭其渊, 梁宏斌, 等. 铁路客运票额预售控制决策模型研究[J]. 铁道学报, 2018, 40(1): 17-23. DOI:10.3969/j.issn.1001-8360.2018.01.03.Liu F X, Peng Q Y, Liang H B, et al. Control and decision model for railway passenger ticket pre-sale[J]. Journal of the China Railway Society, 2018, 40(1): 17-23. DOI:10.3969/j.issn.1001-8360.2018.01.03.(in Chinese)
[14] 史峰, 陈彦, 周文梁, 等. 基于用户平衡分析的铁路旅客列车票额分配计划制定及评价方法[J]. 中国铁道科学, 2008, 29(6): 98-103. DOI:10.3321/j.issn:1001-4632.2008.06.019.Shi F, Chen Y, Zhou W L, et al. Railway passenger train seats allotment plan establishment and evaluation method based on user equilibrium analysis[J]. China Railway Science, 2008, 29(6): 98-103. DOI:10.3321/j.issn:1001-4632.2008.06.019.(in Chinese)
[15] 钱丙益, 帅斌, 陈崇双, 等. 基于旅客buy-up行为的铁路客运专线收益管理模型[J]. 铁道学报, 2013, 35(8): 10-15. DOI:10.3969/j.issn.1001-8360.2013.08.002.Qian B Y, Shuai B, Chen C S, et al. Revenue management model for dedicated passenger line based on passengers' buy-up behavior[J]. Journal of the China Railway Society, 2013, 35(8): 10-15. DOI:10.3969/j.issn.1001-8360.2013.08.002.(in Chinese)
[16] 张力, 蓝伯雄. 基于旅客选择的高速铁路客运收益管理研究[J]. 运筹与管理, 2012, 21(2): 116-125. DOI:10.3969/j.issn.1007-3221.2012.02.018.Zhang L, Lan B X. Revenue management model for high-speed railway based on traveler choice[J]. Operations Research and Management Science, 2012, 21(2): 116-125. DOI:10.3969/j.issn.1007-3221.2012.02.018.(in Chinese)
[17] Hetrakul P, Cirillo C. Accommodating taste heterogeneity in railway passenger choice models based on internet booking data[J]. Journal of Choice Modelling, 2013, 6: 1-16. DOI:10.1016/j.jocm.2013.04.003.
[18] Hetrakul P, Cirillo C. A latent class choice based model system for railway optimal pricing and seat allocation[J]. Transportation Research Part E: Logistics and Transportation Review, 2014, 61: 68-83. DOI:10.1016/j.tre.2013.10.005.
[19] 赵鹏, 李云峰, 李博,等. 基于时段偏好的高铁旅客车次选择行为研究[J]. 北京交通大学学报, 2017, 41(6): 49-54. DOI:10.11860/j.issn.1673-0291.2017.06.008.Zhao P, Li Y F, Li B, et al. Study on the train choice behavior for high-speed railway passengers considering the departure time preference[J]. Journal of Beijing Jiaotong University, 2017, 41(6): 49-54. DOI:10.11860/j.issn.1673-0291.2017.06.008.(in Chinese)
[20] Wang X C, Wang H, Zhang X N. Stochastic seat allocation models for passenger rail transportation under customer choice[J].Transportation Research Part E: Logistics and Transportation Review, 2016, 96: 95-112. DOI:10.1016/j.tre.2016.10.003.
[21] 赵翔, 赵鹏, 姚向明, 等. 高速列车折扣票价与票额分配组合优化模型[J]. 东南大学学报(自然科学版), 2018, 48(4): 759-765. DOI:10.3969/j.issn.1001-0505.2018.04.024.Zhao X, Zhao P, Yao X M, et al. An integrated optimization model of discount fare and ticket allocation for high-speed train[J]. Journal of Southeast University(Natural Science Edition), 2018, 48(4): 759-765. DOI:10.3969/j.issn.1001-0505.2018.04.024.(in Chinese)