Abstract: For the past decade, due to its great challenge and large potential gain, there has been growing interest in the choice-based network revenue management in the academic community as well as the airline industry. An airline company would offer a set of fare products with different prices and restrictions, on a single flight leg or a connecting market with multiple legs. Many products share the same inventory, i.e. seats of a single cabin, and a revenue management system maximizes the total revenue by deciding which products should be available. Traditionally, airline revenue management systems are based on the Independent Demand Model (IDM), in which a customer would consider purchasing a specific product, or leaving when the product is not available. Such an assumption is questioned with the rise of restriction-free pricing introduced by low-cost carriers. Researchers and practitioners then turn to the Discrete Choice Model (DCM), e.g. the well-known Multinomial Logit (MNL) model, which specifies the probability of purchase for each product as a function of the offered product set. There has been extensive literature on the airline network revenue management problem. Compared to the single-leg revenue management problem, the network problem considers both non-stop and connecting customers on the same flight to maximize the overall network revenue. It is widely known that the network problem is difficult to solve even with IDM, not to mention the choice-based counterpart. Our motivation is to propose a simple but attractive solution to integrating the DCM into the network problem.For the single-leg revenue management problem, a technique called the fare transformation is proposed to transform a DCM problem into an equivalent IDM problem, based on the idea of the efficient sets and the efficient frontier of a DCM.
We extend the idea of fare transformation to a specialized network problem with disjoint itineraries, where each segment of the customers only considers a disjoint set of products with the same itinerary. Based on the efficient frontier for each itinerary, we can define the fare transformation in the network problem with disjoint itineraries, which transforms a set of products with DCM into a set of virtual products with IDM whose fares are defined by the slopes between efficient sets in the efficient frontier. We compare the original and the transformed problem in all three steps of the Dynamic Programming Decomposition (DPD) to show their equivalence. The DPD is a legacy solution approach to the network revenue management problem with the IDM assumption, while it is more complicated in the choice-based circumstance. Therefore, with fare transformation, a choice-based network problem with disjoint itineraries can be fit into the legacy revenue management system based on the IDM assumption, and the product substitution effect is taken into account without massive effort or investment.
We prove that the transformed IDM problem is equivalent to the original DCM problem, in the sense that based on the approach of DPD, in any state, an offered product set is the optimal control in the original problem if and only if its corresponding product set is optimal in the transformed problem. Moreover, if the underlying DCM in each itinerary is nested-by-fare-order, we can map each of the original products onto a new IDM product, such that an original product is in the optimal offered product set if and only if its corresponding product is in the optimal set of the IDM problem. Thus, we can easily know whether a product should be available by comparing its transformed fare to the bid price, and this is a legacy optimal control mechanism for the IDM problem. We also discuss the nested-by-fare-order property of a DCM, with which an efficient set of a DCM must be a complete set consisting of all products with fares higher than some threshold value. It is proved that some typical DCMs: (1)the IDM, (2)the lowest open fare (LOF), and (3)the MNL are nested-by-fare-order. We prove that a mixed model of the IDM and the LOF is also nested-by-fare-order. Additionally, we show that a mixed model of the MNL and the IDM / LOF, does not have such a property.

Key words: airline network, revenue management, availability control, discrete choice model, fare transformation

摘要： 近年来,由于其巨大的挑战性与潜在价值,基于离散选择模型的网络收益管理问题受到了学术界和航空业界的持续关注。针对该问题,本文提出在“独立行程”假设下,单航班问题中的运价变换可以推广到网络问题,把离散选择模型转化为相对简单的独立需求模型,并且证明了该变换对“动态规划分解”是完全等价的。特别地,若每个独立行程均符合“按运价嵌套”性质时,可使用经典Bid-price控制方法。进一步地,对于“按运价嵌套”性质,除了已知的独立需求、最低开放运价和MNL(Multinomial Logit)三种模型外,本文证明前两者的混合模型也具备该性质,但包含MNL的混合模型则不具备。

关键词: 航空网络, 收益管理, 舱位控制, 离散选择模型, 运价变换