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

Abstract

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

CLC Number:

U293.1

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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References 23

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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

Optimization model and algorithm for multimodal railway-passenger transportation fares based on demand elasticity

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