A Two-stage Capacity Control Method for Air-rail Passenger Choice Behavior
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摘要: 针对空铁联运容量控制理论缺乏、旅客选择行为复杂化等问题，研究了基于旅客选择行为的空铁联运两阶段容量控制方法。第一阶段建立旅客选择行为模型，通过引入影子吸引力，改进现有选择模型中忽略竞争、选项单一的缺点，建立空铁联运产品选择模型，并基于巢式Logit模型证明其合理性；第二阶段以最大化联运期望收入为目标，建立空铁联运网络容量控制模型，并基于分支定界思想，提出嵌套产品子集下的模型求解算法；最后，针对空-铁网络上150座级机型的容量控制问题进行验证，并对比分析不同竞争强度下的网络期望收入。结果表明：150座航班中有91个舱位分配给航空市场的旅客，有59个舱位分配给联运市场的旅客，网络期望收入为160 600元；在综合考虑替代品竞争的情况下，票价低且竞争性高的产品更具有收入价值；此外，改进后的模型通过引入影子吸引力，捕获了基本吸引力模型和独立需求模型之间的需求，相较于独立需求模型能提高4%左右的期望收入；并且，在非联运产品和联运产品的舱位总数相持的策略下，航空公司可有效应对联运市场的竞争因素影响。Abstract: To address the inadequacy of theories and the complexity of passenger choice behavior, a two-stage capacity control model is established for air-rail intermodal capacity control. In the first stage, an air-rail intermodal passenger choice model is established. The shadow attraction value is introduced to address the shortcomings of existing choice models that overlook competition and limit passengers'choices. Then, the proposed choice model is verified based on the nested Logit model. In the second stage, a network capacity control model is established by maximizing intermodal expected revenue. The algorithm is proposed based on the branch and bound method, which is used to rationalize product offerings. The case study is carried out by a flight with 150 seats. A comparative analysis is also conducted to verify the expected revenue under different levels of competition. The results indicate that 91 seats are allocated to passengers in the aviation market and 59 seats to passengers in the intermodal market. The total expected revenue is 160 600 RMB. To airlines, products with lower price but stronger competitiveness are more valuable when considering product competition. By introducing shadow attraction value, the two-stage model captures the demand between the basic attraction model and independent demand model. Compared to the independent demand model, the model can increase the expected revenue by around 4%. The study illustrates that airlines can effectively cope with the impact of competition by maintaining the total number of seats for non-intermodal products and intermodal products.
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表 1 产品和对应价格
Table 1. Products and corresponding prices
细分市场 产品序号 产品 价格/元 说明 l = 1 j = 1 ABH 1 200 商务舱（Z） j = 2 ABL1 900 经济舱（Y） j = 3 ABL2 700 经济舱（Q） h = 2 j = 1 ABCH1 1 400 商务舱（Z）+一等座 j = 2 ABCH2 1 300 商务舱（Z）+二等座 h = 3 j = 1 ABCL1 1 000 经济舱（Y）+二等座 j = 2 ABCL2 900 经济舱（Q）+二等座 
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表 2 产品吸引力和影子吸引力
Table 2. Products attraction value and shadow attraction value
$(v, w) $ $ A B_H$ $A B_{L 1}$ $A B_{L 2}$ $A B C_{H 1}$ $A B C_{H 2}$ $A B C_{L 1}$ $A B C_{L 2}$ 不购买 l = 1 （6，1） （8，2） （9，2） 1 h = 2 （10，2） （9，2） 2 h = 3 （5，1） （10，1） 2
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表 3 模型输出结果
Table 3. Output results of model
数量/个 $ A B_H$ $A B_{L 1}$ $A B_{L 2}$ $A B C_{H 1}$ $A B C_{H 2}$ $A B C_{L 1}$ $A B C_{L 2}$ 网络期望收入/元 l = 1 45 46 0 95 400 h = 2 18 30 400 h = 3 24 12 34 800 总计 45 46 0 5 18 24 12 160 600
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表 4 各细分市场上甲航空公司提供的产品子集及时长比例
Table 4. Product assortments in each segment and the optimal proportion of offering time
细分市场 产品子集 时长比例/% l=1 $S_{11}=\left\{A B_H\right\}$ 16.04 $S_{12}=\left\{A B_H, A B_{L 1}\right\}$ 81.46 $S_{13}=\left\{A B_H, A B_{L I}, A B_{L 2}\right\}$ 0 h=2 $S_{21}=\left\{A B C_{H 2}\right\}$ 65.00 $S_{22}=\left\{A B C_{H 2}, A B C_{H 1}\right\}$ 35.00 h=3 $S_{31}=\left\{A B C_{L\}}\right\}$ 57.60 $S_{32}=\left\{A B C_{L 1}, A B C_{L 2}\right\}$ 40.80
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表 5 不同比值参数及对应模型输出结果
Table 5. Output of model for different parameters
ρ 网络期望收入/元 舱位数量/个 $ A B_H$ $A B_{L 1}$ $A B_{L 2}$ $A B C_{H 1}$ $A B C_{H 2}$ $A B C_{L 1}$ $A B C_{L 2}$ 0.0 180 571 103 0 0 25 0 22 0 0.1 174 101 82 0 0 14 13 20 21 0.2 167 080 61 18 0 14 13 15 29 0.3 163 540 49 30 0 14 13 15 29 0.4 161 596 43 36 0 14 13 15 29 0.5 160 367 39 40 0 14 13 15 29 0.6 159 520 36 43 0 14 13 15 29 0.7 158 901 34 45 0 14 13 15 29 0.8 157 728 32 43 4 14 13 15 29 0.9 156 777 31 41 7 14 13 15 29 1.0 156 008 30 40 9 14 13 15 29
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