基于需求弹性的多模式铁路客运票价优化模型及算法

doi:10.3976/j.issn.1002-4026.20230168

摘要/Abstract

摘要：

为增强铁路客运市场竞争力、提高其运营收入,对多模式铁路客运票价的多目标系统优化问题进行了研究。采用变分不等式模型对不同铁路客运产品客运需求之间的平衡关系进行描述,采用灵敏度分析的方法给出了多模式铁路客运产品需求弹性的计算方法,并构建了多模式铁路客运的市场需求函数;在此基础上,综合考虑了铁路客运企业的市场需求、客运收入、利润以及旅客出行费用等多个优化目标,提出了多目标双层规划模型来描述多模式铁路客运票价的系统优化问题。最后,采用北京至天津的真实铁路客运数据对提出的模型进行验证。结果表明本文提出的票价优化方法可以有效兼顾客运需求、客运收入以及利润等多个指标,为铁路客运部门在不同市场竞争阶段制定科学合理的铁路客运票价体系提供参考和支撑。

关键词: 铁路客运, 铁路客运票价, 需求弹性, 多目标, 双层规划

Abstract:

To improve the competitiveness of the railway-passenger transportation market and increase its operational revenue, this study investigates the multiobjective system optimization issue of multimodal railway-passenger transportation fares. A mathematical model was used to describe the equilibrium relationship among the demands of different railway-passenger transportation products. Sensitivity analysis was performed to provide a calculation method for the demand elasticity of multimodal railway-passenger transportation products, and a market demand function for multimodal railway-passenger transportation was formulated. Considering multiple optimization objectives such as market demand, passenger transportation revenue, and profit of railway-passenger transportation enterprises along with passenger transportation costs, we proposed a multiobjective bi-level planning model for describing the system optimization issue of multimodal railway-passenger transportation fares. Finally, we used real passenger transportation data of the railway line between Beijing and Tianjin to validate the proposed model. The results show that the proposed method can effectively balance multiple objectives such as passenger transportation demand, passenger transportation revenue, and profit, providing reference and support for railway-passenger transportation departments to develop scientifically reasonable fare systems in different market competition stages.

Key words: railway-passenger transportation, railway-passenger fare, demand elasticity, multi-objective, bi-level planning

中图分类号:

U293.1

王红印, 袁媛, 崔鸿蒙, 郑宣传, 四兵锋. 基于需求弹性的多模式铁路客运票价优化模型及算法[J]. 山东科学, 2024, 37(5): 69-78.

WANG Hongyin, YUAN Yuan, CUI Hongmeng, ZHENG Xuanchuan, SI Bingfeng. Optimization model and algorithm for multimodal railway-passenger transportation fares based on demand elasticity[J]. Shandong Science, 2024, 37(5): 69-78.

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客运方式	C列车	D列车	G列车	KTZ列车	普通列车
需求分担率/%	81.93	0.29	10.35	6.14	1.29
需求分担量/(万人次·d^-1)	36 972	125	4 673	2 773	584
平均时耗/min	38	38	41	114	114
平均票价/元	54.5	54.5	54.5	21.5	18.5
最低票价率/(元·人^-1·km^-1)	0.25	0.33	0.33	0.22	0.22
运营里程/km	120	120	120	137	137
最高限价/元	60	65	65	50	50

参数	估计值	标准误差	t分布	显著性水平
α	0.208 9	0.032	-4.320 1	0.001
β	0.197 8	0.044	-5.344 1	0.002

客运方式	C列车	D列车	G列车	KTZ列车	普通列车
C列车	-0.37	0.88	0.73	0.09	0.04
D列车	0.85	-0.81	0.64	0.04	0.07
G列车	0.69	0.52	-0.55	0.10	0.04
KTZ列车	0.02	0.02	0.05	-0.23	0.39
普通列车	0.01	0.02	0.02	0.27	-0.95

优化目标	不同目标下的最优票价/元					F₁	F₂	F₃
优化目标	C	D	G	KTZ	普通	F₁	F₂	F₃
需求最大化	30	40	40	30	30	5.145 2	1.621 8	0
收入最大化	60	58	62	52	30	4.189 6	2.530 5	0.124 4
利润最大化	60	65	65	50	40	4.154 6	2.489 1	0.128 2

λ₁	λ₂	λ₃	不同目标下的最优票价/元					F₁	F₂	F₃
λ₁	λ₂	λ₃	C	D	G	KTZ	普通	F₁	F₂	F₃
1/3	1/3	1/3	60	52	60	44	30	4.242 5	2.491 0	0.121 8
0.1	0.3	0.6	60	65	65	50	30	4.175 6	2.505 2	0.125 3
0.1	0.6	0.3	60	60	65	50	30	4.178 6	2.505 4	0.125 2
0.3	0.1	0.6	60	60	65	50	30	4.178 6	2.505 4	0.125 2
0.3	0.6	0.1	60	50	56	44	30	4.268 9	2.480 6	0.120 0
0.6	0.1	0.3	34	40	40	30	30	5.051 1	1.749 3	0.023 4
0.6	0.3	0.1	36	40	40	30	30	5.004 1	1.810 3	0.030 9