﻿ 机票定价与舱位控制两阶段决策方法
 控制与决策  2019, Vol. 34 Issue (6): 1293-1299 0

### 引用本文 [复制中英文]

[复制中文]
GAO Jin-min, LE Mei-long, QU Lin-chi. Two-stage decision approach of air pricing and seat inventory control[J]. Control and Decision, 2019, 34(6): 1293-1299. DOI: 10.13195/j.kzyjc.2017.1474.
[复制英文]

### 文章历史

1. 上海工程技术大学 管理学院，上海 201620;
2. 上海海事大学 经济管理学院，上海 201306;
3. 南京航空航天大学 民航学院，南京 211106

Two-stage decision approach of air pricing and seat inventory control
GAO Jin-min 1,2, LE Mei-long 3, QU Lin-chi 2
1. School of Management, Shanghai University of Engineering Science, Shanghai 201620, China;
2. School of Economics & Management, Shanghai Maritime University, Shanghai 201306, China;
3. College of Civil Aviation, Nanjing University of Aeronautics & Astronautics, Nanjing 211106, China
Abstract: For the joint decision making problem of pricing and seat inventory control in airline revenue management, a two-stage decision approach is proposed. Firstly, corresponding joint models are established and analyzed with the good of maximizing the total revenue, including non-nested models(the deterministic model and the stochastic model) and nested models. Some conclusions are obtained through solving and simulating the models. For ticket pricing, the price from the stochastic model is the highest. The second highest is that from the nested model. The price from the deterministic model is the lowest. For the booking limit of low fare classes, the stochastic model is the strictest. The second strictest is deterministic model. The nested model is the loosest among them. The finally simulation results show that, the nested model produces the highest total revenue, and for non- nested models, the deterministic model does not always outperform the stochastic model. In order to response to the complexity of solving the large-scale example of the nested model, we regard the price from the non-nested model as the input price of the nested model respectively and obtain corresponding seat allocation results. Also, two groups of two-stage strategies of pricing and seat inventory control are produced, which are verified by example simulation. The results show that, the two-stage strategy from the combination of the stochastic model and the nested model performs better, and it can generate total revenue closer to the optimal level.
Keywords: pricing of air ticket    seat inventory control    joint decision making    non-nested model    nested model    two-stage strategy
0 引言

Weatherford[6]在传统收益管理的基础上, 考虑现实状况, 将价格同时作为决策变量, 探讨了3种不同类型的联合决策问题, 依次为:不考虑旅客转移需求的分块舱位控制、不考虑旅客转移需求的序列嵌套舱位控制以及考虑旅客需求转移的序列嵌套舱位控制.该研究针对各问题建立了相应的模型, 并且对增加优化条件所能提高的总收益与相应增加的求解时间之间进行了敏感性分析. Kuyumcu等[7]和Bertsimas[8]都基于整个航线网络来研究机票定价和舱位控制联合决策问题. Chew等[9]针对两阶段的单一产品销售问题提出了一个联合优化方法, 假设产品需求是不确定的, 并且需求期望值是其自身价格的线性函数.该研究基于目标收益函数的凹性质提出了确定最优价格和预定限制的迭代算法, 并进一步考虑了多阶段优化的情况. Cizaire[10]提出了同时求解最优票价和订座限制的几种方法, 首先假设需求是确定的, 针对两种票价等级和两个订票阶段的收益优化问题建立了确定性数学规划模型; 然后针对需求不确定的情况建立了随机优化模型, 分析了票价与订座限制对所接受订票总数量的综合影响, 指出相对于传统收益管理联合决策模型能使总收益提高3 %~4 %; 最后将订票阶段拓展到多个订票阶段的情况.之后, Cizaire等[11]又将票价和订票限制同时作为决策变量, 对两种票价等级和两个订票阶段下的收益管理问题进行了研究.此外, 一部分学者考虑竞争因素, 对相关问题展开了研究, 但是由于竞争模型的复杂性, 大部分研究只涉及两家公司, 具体可参考文献[12-15].

1 模型假设和符号

1) 各票价等级的旅客需求是不确定的, 需求期望只与其自身的价格相关;

2) 未被满足的旅客需求被视为收益流失, 不存在需求转移.

2 非嵌套模型 2.1 随机性数学规划模型

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2.2 确定性数学规划模型

 (4)
 (5)
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3 嵌套模型

3.1 两等级票价嵌套模型

 图 1 两种票价嵌套示意图

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 (8)
 (9)

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3.2 多等级票价嵌套模型

 图 2 多种票价嵌套示意图

 图 3 3种票价等级建模情况分析
 图 4 K种票价等级建模情况分析

 (14)
 (15)

4 算例结果分析

4.1 定价与座位分配结果

4.2 仿真收益结果

 图 5 联合策略仿真结果

 图 6 两阶段策略仿真结果

 图 7 仿真结果对比
 图 8 收益差距对比
5 结论

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