考虑转移因素的航空收益管理
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摘要
随着中国经济的高速发展,快速交通成为人们出行的首选。为了满足日益增长的交通需求,近几年来,中国大力发展航空业。例如,中国两大城市上海和北京之间,每天就有不少于40次航班。但由于机场位置较偏；城市离机场很远；旅客不能在不同的航班之间自由签转；地面服务流程比较繁杂,事实上大多数旅客难以用最短的时间完成京沪两地机场之间的航空旅行,航空旅行“快”的特征大打折扣。为了改变这种局面,同时为了应对铁路(动车,高铁等)持续提速带来的竞争压力,2007年8月,在中国民用航空总局牵头下,中国国际航空、中国东方航空、上海航空、中国南方航空和海南航空等五家航空公司共同参与,开通了一些新的航线。按规定,凡乘坐这些新航线的旅客将享有专用办票柜台、安检通道、候机区域、登机口和行李提取区域等多项便利服务等。最重要的一点是：旅客随到随走,不受航班限制,就象坐公交车一样,故形象地称之为“京沪空中快线”。但运行多年来,并没有达到预期效果,经常出现大量乘客买了票却登不了机的现象。专家指出最大原因是机票超订(overbooking)的随意性：反正半小时一班,又可以自由签转,超没超订也没人监管,各航空公司当然会随意卖票了。因而在考虑转移因素下怎样确定超订策略和最优订票策略是解决该问题的关键。
本文就是根据以上背景,在考虑不同假设的前提下,建立了多个动态规划模型。通过对模型的理论分析,找出最优订票策略。然后,基于一些算例,验证理论结果同时给出具体的最优订票策略,从而说明了这些方法的可行性。具体内容如下：
第一章,介绍了收益管理的发展历史和研究现状。讨论了本文所研究问题的背景和意义。
第二章,讨论了在不考虑转移因素下,怎样制定最优订票策略。首先,对每个航班建立了对应的连续型模型,同时给出了模型所满足的最优性方程。然后讨论了怎样求解该最优性方程。最后,证明了价值函数的一些性质,如价值函数的凹性,价值函数关于已订出票数的递减性。这些为后面讨论在考虑转移因素下一些相关性质做好准备。
第三章,讨论在考虑单向转移因素(早起飞航班的乘客允许转移到晚起飞航班)下,怎样制定最优订票策略。这里采用了三种方法：(1)虚拟法,即：先采用虚拟手段,也就是对除了最后一个航班的所有航班,在该航班起飞时刻到最后一个航班起飞时刻间构造虚拟订票和退票过程(订票参数和退票参数都为零),使所有航班在同一时刻(最后航班的起飞时刻)起飞。然后在此基础上讨论问题。该方法中转移因素一次性在终点函数的定义中得到考虑。(2)分割法,即：先利用每个航班的起飞时刻将从卖票开始到最后一个航班离开的整个时间段分成有限段,每段对应一个子系统,然后按时间逆序,从最后一个子系统倒退到第一个子系统,这样整个大系统就得到了研究。该方法中的转移因素在每个子系统终点函数的定义中得到考虑。(3)简化法,即：除了第一个航班以外的每个航班用相邻的早起飞的航班的起飞时刻把整个售票时段分为两段,第一段完全不考虑转移因素。在第一段运行结果的基础上,采用优化方法求出转移量,基于这个转移量讨论第二段。不管是哪种方法,都取得了一些性质,如：价值函数的凹性；价值函数的超模性(Supermodular)；转移因素对超订限的影响情况,即转移因素使最早起飞航班的超订限不减,最晚起飞航班的超订限不增,中间航班的超订限不定；考虑转移因素所得的总收益不小于不考虑转移因素所得的总收益以及各航班超订限的上界等。
第四章,讨论在考虑双向转移因素(早起飞的航班的乘客可以转移到晚起飞的航班,同时晚起飞航班的乘客在早起飞航班的起飞时刻如果在机场也愿意早走的话且早起飞航班有空位,也允许转移到早起飞的航班)下,怎样制定最优订票策略。这里采用了两种方法：(1)分割法,该方法类似于上一章的第二种方法,主要区别在于,每个子系统的终点函数中要考虑两个方向的转移。(2)简化法,该方法类似于上一章的第三种方法,主要区别在于,在每个终点要考虑双向转移。不管是哪种方法,都取得了一些性质,如：价值函数的凹性；价值函数的超模性；考虑转移因素所得的总收益不小于不考虑转移因素所得的总收益以及各航班超订限的上界等。
第五章,由于前几章中所涉及到的理论证明比较复杂且其中有一定的关联性,故将它们有机的组织在一起构成一章。
With the rapid development of Chinese economy, the amount of passengers by air grows dramatically. In order to meet this challenge, Chinese airport administration devel-ops aircraft industry rapidly in recent years. For example, in the line between Shanghai and Beijing, there are more than forty airlines each day. Because the airports are far from the cities, the passengers are not permitted to transfer between different airlines and the check-in procedures are intricate, the most passengers are unable to travel between two cities quickly. In order to reverse the tide and cope with competition from the railway, many airlines such as China Airlines, China Eastern Airlines, China Southern Airlines and Shanghai Airlines are implementing a policy named "quick route in the line between Shanghai and Beijing" on August 2007. The essential point of this policy is that the passengers can board any flights if there have. However, this policy have not obtained the expectation effect. As some experts pointed out the main reason was that the overbooking was out of control.
Basing on aforementioned background and some different assumptions, several stochastic dynamic programming models are constructed firstly. Secondly, from these models, some theory results and optimal booking policy are obtained. Lastly, these the-ory results and optimal booking policy are gained through some numerical experiments. The detailed content are displayed as follows:
Chapter 1, the history of revenue management, its present research situation and perspectives are introduced. At the same time, the background and significance of the issue discussed in this paper are investigated.
Chapter 2, how to implement the booking policy without considering transference option are discussed. Specifically, basing on the optimality equation, some properties of value function are proved, such as the value function is a decreasing concave function of the number of the booked ticket. These conclusions are prepared well for discussing the relative properties when the transference option is considered in the later chapters.
Chapter 3, how to implement the booking policy with uni-directional transference option are discussed. Here three methods are adopted. The first one is that, we make all flights' departure time is the same (equal to the last flight's departure time) by means of constructing virtual booking process and cancelation process to all flights but the last one from its departure time to the last flight's departure time, and then the aforementioned question is discussed using the traditional method. The second one is that, we separate the whole system into finite subsystem from each flight's departure time, and then each subsystem is discussed by using the traditional method. The third one is an approximative model of the first two models, curse of dimensionality is avoided. Basing on each method, some properties are obtained, such as:value function is a decreasing concave function of the number of the booked ticket; the overbooking limit of flight 1 under the policy of transference is greater than that without performing such policy; if the transference policy is adopted, the total revenue will not decrease and so on.
Chapter 4, how to implement the booking policy with bilateral-directional transfer-ence option arc discussed. Here two methods are adopted. The first one is similar to the second method in the chapter 3. The only difference is the definition of each subsystem's terminal function. The second one is an approximative model of the first model, which is similar to the third method in the chapter 3, curse of dimensionality is avoided. Basing on each method, some properties are obtained, such as:value function is a decreasing concave function of the number of the booked ticket; if the transference policy is adopted, the total revenue will not decrease and so on.
Chapter 5, because the proofs of some conclusions from chapter 2 to chapter 4 are complicated and correlative, they are organized rationally and constitute this chapter.
本文就是根据以上背景,在考虑不同假设的前提下,建立了多个动态规划模型。通过对模型的理论分析,找出最优订票策略。然后,基于一些算例,验证理论结果同时给出具体的最优订票策略,从而说明了这些方法的可行性。具体内容如下：
第一章,介绍了收益管理的发展历史和研究现状。讨论了本文所研究问题的背景和意义。
第二章,讨论了在不考虑转移因素下,怎样制定最优订票策略。首先,对每个航班建立了对应的连续型模型,同时给出了模型所满足的最优性方程。然后讨论了怎样求解该最优性方程。最后,证明了价值函数的一些性质,如价值函数的凹性,价值函数关于已订出票数的递减性。这些为后面讨论在考虑转移因素下一些相关性质做好准备。
第三章,讨论在考虑单向转移因素(早起飞航班的乘客允许转移到晚起飞航班)下,怎样制定最优订票策略。这里采用了三种方法：(1)虚拟法,即：先采用虚拟手段,也就是对除了最后一个航班的所有航班,在该航班起飞时刻到最后一个航班起飞时刻间构造虚拟订票和退票过程(订票参数和退票参数都为零),使所有航班在同一时刻(最后航班的起飞时刻)起飞。然后在此基础上讨论问题。该方法中转移因素一次性在终点函数的定义中得到考虑。(2)分割法,即：先利用每个航班的起飞时刻将从卖票开始到最后一个航班离开的整个时间段分成有限段,每段对应一个子系统,然后按时间逆序,从最后一个子系统倒退到第一个子系统,这样整个大系统就得到了研究。该方法中的转移因素在每个子系统终点函数的定义中得到考虑。(3)简化法,即：除了第一个航班以外的每个航班用相邻的早起飞的航班的起飞时刻把整个售票时段分为两段,第一段完全不考虑转移因素。在第一段运行结果的基础上,采用优化方法求出转移量,基于这个转移量讨论第二段。不管是哪种方法,都取得了一些性质,如：价值函数的凹性；价值函数的超模性(Supermodular)；转移因素对超订限的影响情况,即转移因素使最早起飞航班的超订限不减,最晚起飞航班的超订限不增,中间航班的超订限不定；考虑转移因素所得的总收益不小于不考虑转移因素所得的总收益以及各航班超订限的上界等。
第四章,讨论在考虑双向转移因素(早起飞的航班的乘客可以转移到晚起飞的航班,同时晚起飞航班的乘客在早起飞航班的起飞时刻如果在机场也愿意早走的话且早起飞航班有空位,也允许转移到早起飞的航班)下,怎样制定最优订票策略。这里采用了两种方法：(1)分割法,该方法类似于上一章的第二种方法,主要区别在于,每个子系统的终点函数中要考虑两个方向的转移。(2)简化法,该方法类似于上一章的第三种方法,主要区别在于,在每个终点要考虑双向转移。不管是哪种方法,都取得了一些性质,如：价值函数的凹性；价值函数的超模性；考虑转移因素所得的总收益不小于不考虑转移因素所得的总收益以及各航班超订限的上界等。
第五章,由于前几章中所涉及到的理论证明比较复杂且其中有一定的关联性,故将它们有机的组织在一起构成一章。
With the rapid development of Chinese economy, the amount of passengers by air grows dramatically. In order to meet this challenge, Chinese airport administration devel-ops aircraft industry rapidly in recent years. For example, in the line between Shanghai and Beijing, there are more than forty airlines each day. Because the airports are far from the cities, the passengers are not permitted to transfer between different airlines and the check-in procedures are intricate, the most passengers are unable to travel between two cities quickly. In order to reverse the tide and cope with competition from the railway, many airlines such as China Airlines, China Eastern Airlines, China Southern Airlines and Shanghai Airlines are implementing a policy named "quick route in the line between Shanghai and Beijing" on August 2007. The essential point of this policy is that the passengers can board any flights if there have. However, this policy have not obtained the expectation effect. As some experts pointed out the main reason was that the overbooking was out of control.
Basing on aforementioned background and some different assumptions, several stochastic dynamic programming models are constructed firstly. Secondly, from these models, some theory results and optimal booking policy are obtained. Lastly, these the-ory results and optimal booking policy are gained through some numerical experiments. The detailed content are displayed as follows:
Chapter 1, the history of revenue management, its present research situation and perspectives are introduced. At the same time, the background and significance of the issue discussed in this paper are investigated.
Chapter 2, how to implement the booking policy without considering transference option are discussed. Specifically, basing on the optimality equation, some properties of value function are proved, such as the value function is a decreasing concave function of the number of the booked ticket. These conclusions are prepared well for discussing the relative properties when the transference option is considered in the later chapters.
Chapter 3, how to implement the booking policy with uni-directional transference option are discussed. Here three methods are adopted. The first one is that, we make all flights' departure time is the same (equal to the last flight's departure time) by means of constructing virtual booking process and cancelation process to all flights but the last one from its departure time to the last flight's departure time, and then the aforementioned question is discussed using the traditional method. The second one is that, we separate the whole system into finite subsystem from each flight's departure time, and then each subsystem is discussed by using the traditional method. The third one is an approximative model of the first two models, curse of dimensionality is avoided. Basing on each method, some properties are obtained, such as:value function is a decreasing concave function of the number of the booked ticket; the overbooking limit of flight 1 under the policy of transference is greater than that without performing such policy; if the transference policy is adopted, the total revenue will not decrease and so on.
Chapter 4, how to implement the booking policy with bilateral-directional transfer-ence option arc discussed. Here two methods are adopted. The first one is similar to the second method in the chapter 3. The only difference is the definition of each subsystem's terminal function. The second one is an approximative model of the first model, which is similar to the third method in the chapter 3, curse of dimensionality is avoided. Basing on each method, some properties are obtained, such as:value function is a decreasing concave function of the number of the booked ticket; if the transference policy is adopted, the total revenue will not decrease and so on.
Chapter 5, because the proofs of some conclusions from chapter 2 to chapter 4 are complicated and correlative, they are organized rationally and constitute this chapter.
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