New Directions in Revenue Management Research

Research in revenue management is rapidly changing as the environment in which firms operate changes. The Internet, the adoption of new information technologies, and other market forces are driving a new wave of research in revenue management. At the same time, more and more industries are adapting the tools of revenue management to their needs. Promising research directions are more sophisticated models of consumer behavior, more general models and understanding of rivalry, and more general pricing mechanisms. These are important issues for today's revenue managers and promising areas for both theoretical and empirical research.     

服务科学管理与工程：一个正在兴起的领域

20世纪80年代以来,服务日趋重要,并有占据全球经济主导地位之势。服务科学旨在通过科学的形式化方法对服务展开跨学科的系统研究,目前正处于兴起阶段。回顾了服务经济在全球快速成长的形势,说明了服务科学研究的必要性、紧迫性及其兴起过程。在重点讨论了服务科学的研究对象"服务"的基础上,详细阐述了服务科学的概念与目标,说明了服务科学的核心议题和研究方向。     

高速铁路客运专线的收益管理模型

本文在分析铁路客运收益管理的研究进展的基础上,提出了一个适合铁路客运专线的收益管理优化模型。模型以列车运营总收益最大化为目标,优化列车的席位控制和发车间隔,将席位分配与运营能力优化统一在一个模型中。利用随机生成数据进行的模型试验表明,模型可以在较短的时间内求解较大规模的收益管理优化问题。     

Optimal Dynamic Upgrading in Revenue Management

We consider a revenue management problem involving a two compartment aircraft flying a single leg, with no cancellations or over‐booking. We apply the practice of transforming a choice revenue management model into an independent demand model. Within this assumed independent model, there are two sets of demands, business and economy, each with multiple fare class products. A business passenger can only be accepted into business. An economy passenger can be accepted into economy or upgraded into business. We define a two‐dimensional dynamic program (DP) and show that the value function is sub‐modular and concave in seat availability in the two compartments. Thus the bid prices are non‐decreasing with respect to these state variables. We use this result to propose an exact algorithm to solve the DP. Our numerical investigation suggests that in contrast to standard backward induction, our method could be included in production revenue management systems. Further, when the economy compartment is capacity constrained, we observe a substantial monetary benefit from optimal dynamic upgrading compared to the static upgrading procedures currently used in practice.     

有多个销售渠道的连续时间收益管理问题研究

研究了有多个销售渠道的连续时间收益管理问题.利用最优控制理论,建立了最大期望收益函数所满足的HJB最优方程,证明了最大期望收益是剩余商品数量的递增凹函数、是销售时间的递减凹函数,最优定价策略随剩余商品数量及销售时间递减;得到了不同销售渠道的最优定价之间所满足的一个关系式.最后,利用数值仿真的方法对不同销售渠道差别定价的效果进行了讨论.     

Using Prices More Realistically as Decision Variables in Perishable-Asset Revenue Management Problems

This paper addresses a new slant to a problem which is general to many of the transportation industries—perishable asset revenue management. Traditional approaches have assumed that prices are fixed and solved for the optimal allocation quantities. Our approach recognizes that prices of the different classes affect demand and should therefore be included as decision variables to be optimized. We solve three different types of problems: (a) up to n price classes, distinct asset control mechanism, and no diversion, (b) up to 3 price classes, serial nested asset control mechanism, and no diversion, (c) up to 3 price classes, serial nested asset control mechanism, and diversion. Analytical results are provided in most cases and examples illustrate the results as well as the time required to solve these complex problems. Finally we look at the tradeoff involved between computational time and expected contribution when using heuristic decisions obtained from less realistic assumptions relative to the true optimal decisions. On average, the suboptimality ranged from 3.19% to 4.88% with a corresponding decrease in computing time required on the order of several minutes. Some trends are presented to help determine a priori which type of problems would tend to benefit most from the more accurate formulation. This should help managers decide when it is worth the extra computing time to come up with the true optimal solution.     

Revenue and Cost Management for Remanufactured Products

This paper considers pricing and remanufacturing strategy of a firm that decides to offer both new and remanufactured versions of its product in the market and is concerned with demand cannibalization. We present a model of demand cannibalization and a behavioral study that estimates a key modeling parameter: a fraction of consumers who switch from new to remanufactured product. As we show, this fraction has an inverted‐U shape, and, thus, the underlying consumer behavior cannot be modeled using the standard methodologies that rely on consumers' willingness to pay (WTP). We find that by incorporating the inverted‐U‐shaped consumer behavior, the firm remanufactures under broader conditions, charges a much lower price, and typically remanufactures more units—leading to an increase of profits from remanufacturing by up to a factor of two as compared with making decisions based on the WTP only. Lastly, we find that the behavior of the low‐price market segment plays an important role because the firm reacts to it differently than the WTP‐based logic would suggest.     

On the Use of Buy Up as a Model of Customer Choice in Revenue Management

We consider settings in which a revenue manager controls bookings over a sequence of flights. The revenue manager uses a buy‐up model to select booking limits and updates estimates of the model parameters as data are accumulated. The buy‐up model we consider is based upon a simple model of customer choice, wherein each low‐fare customer who is not able to purchase a low‐fare ticket will, with a fixed probability, “buy up” to the high fare, independent of everything else. We analyze the evolution of the parameter estimates (e.g., the buy‐up probability) and chosen booking limits in situations where the buy‐up model is misspecified, that is, in situations where there is no setting of its parameters for which its objective function gives an accurate representation of expected revenue as a function of the booking limit. The analysis is motivated by the common situation in which a revenue manager does not know precisely how customers behave but nevertheless uses a parametric model to make decisions. Under some assumptions, we prove that the booking limits and parameter estimates converge and we compare the actual expected revenue at the limiting values with that associated with the booking limits that would be chosen if the revenue manager knew the actual behavior of customers. The analysis shows that the buy‐up model often works reasonably well even when it is misspecified, and also reveals the importance of understanding how parameter estimates of misspecified models vary as functions of decisions.     

收益的定价管理在网络空间租赁中的应用

将收益管理技术引入网络空间租赁领域,通过对网络空间特点的分析,得出影响供应商定价的5种因素:软硬件配置及基础设施建设、服务、租赁空间的大小、租赁时间和技术进步,并通过相关数据说明这些因素对供应商定价产生的影响。将收益管理与网络租赁产品价格设计联系起来,简要阐述了网络产品价格设计的全过程,并针对当前价格设计中存在的问题,提出了几种有效的解决方法。     

Randomization Approaches for Network Revenue Management with Customer Choice Behavior

In this study, we present new approximation methods for the network revenue management problem with customer choice behavior. Our methods are sampling‐based and so can handle fairly general customer choice models. The starting point for our methods is a dynamic program that allows randomization. An attractive feature of this dynamic program is that the size of its action space is linear in the number of itineraries, as opposed to exponential. It turns out that this dynamic program has a structure that is similar to the dynamic program for the network revenue management problem under the so called independent demand setting. Our approximation methods exploit this similarity and build on ideas developed for the independent demand setting. We present two approximation methods. The first one is based on relaxing the flight leg capacity constraints using Lagrange multipliers, whereas the second method involves solving a perfect hindsight relaxation problem. We show that both methods yield upper bounds on the optimal expected total revenue. Computational experiments demonstrate the tractability of our methods and indicate that they can generate tighter upper bounds and higher expected revenues when compared with the standard deterministic linear program that appears in the literature.     

Scalable Dynamic Bid Prices for Network Revenue Management in Continuous Time

This study develops an approximate optimal control problem to produce time‐dependent bid prices for the airline network revenue management problem. The main contributions of our study are the analysis of time‐dependent bid prices in continuous time and the use of splines to modify the problem into an approximate second‐order cone program (ASOCP). The spline representation of bid prices permits the number of variables to depend solely on the number of resources and not on the size of the booking horizon. The advantage of this framework is the ASOCP's scalability, which we demonstrate by solving for bid prices on an industrial‐sized network. The numerical experiments highlight the ASOCP's ability to solve industrial sized problems in seconds.     

A Comparison of Unconstraining Methods to Improve Revenue Management Systems

Asuccessful revenue management system requires accurate demand forecasts for each customer segment. The forecasts are used to set booking limits for lower value customers to ensure an adequate supply for higher value customers. The very use of booking limits, however, constrains the historical demand data needed for an accurate forecast. Ignoring this interaction leads to substantial penalties in a firm's potential revenues. We review existing unconstraining methods and propose a new method that includes some attractive properties not found in the existing methods. We evaluate several of the common unconstraining methods against our proposed method by testing them on intentionally constrained simulated data. Results indicate our proposed method outperforms other methods in two of three data sets. We also test the revenue impact of our proposed method, expectation maximization (EM), and “no unconstraining” on actual booking data from a hotel/casino. We show that performance varies with the initial starting protection limits and a lack of unconstraining leads to significant revenue losses.     

基于收益管理的高灵活性产品两阶段销售模型研究

Gallego和Phillps研究了航空公司销售由2种产品组成的灵活性产品,顾客购买了这种产品后,将由航空公司根据情况决定所乘班次.基于此并将此推广到更加灵活性的产品组合,即同时销售3种产品和它们的组合,建立了3种产品的随机动态模型.通过模型求解和算例,发现在一定条件下企业销售更高灵活性的产品组合可以分担风险,并增加企业的期望收益.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

Revenue Management of Reusable Resources with Advanced Reservations

We consider a revenue management problem wherein the seller is endowed with a single type resource with a finite capacity and the resource can be repeatedly used to serve customers. There are multiple classes of customers arriving according to a multi‐class Poisson process. Each customer, upon arrival, submits a service request that specifies his service start time and end time. Our model allows customer advanced reservation times and services times in each class to be arbitrarily distributed and correlated. Upon arrival of each customer, the seller must instantaneously decide whether to accept this customer's service request. A customer whose request is denied leaves the system. A customer whose request is accepted is allocated with a specific item of the resource at his service start time. The resource unit occupied by a customer becomes available to other customers after serving this customer. The seller aims to design an admission control policy that maximizes her expected long‐run average revenue. We propose a policy called the ε‐perturbation class selection policy (ε‐CSP), based on the optimal solution in the fluid setting wherein customers are infinitesimal and customer arrival processes are deterministic, under the restriction that the seller can utilize at most (1 − ε) of her capacity for any ε ∈ (0, 1). We prove that the ε‐CSP is near‐optimal. More precisely, we develop an upper bound of the performance loss of the ε‐CSP relative to the seller's optimal revenue, and show that it converges to zero with a square‐root convergence rate in the asymptotic regime wherein the arrival rates and the capacity grow up proportionally and the capacity buffer level ε decays to zero.     

An Enhanced Concave Program Relaxation for Choice Network Revenue Management

The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice‐set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP‐hard. In this study, starting with a concave program formulation called SDCP that is based on segment‐level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition, we propose a natural direct tightening of the SDCP called , and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the data sets, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.     

Revenue Management for Intermodal Transportation: The Role of Dynamic Forecasting

We study a joint capacity leasing and demand acceptance problem in intermodal transportation. The model features multiple sources of evolving supply and demand, and endogenizes the interplay of three levers—forecasting, leasing, and demand acceptance. We characterize the optimal policy, and show how dynamic forecasting coordinates leasing and acceptance. We find (i) the value of dynamic forecasting depends critically on scarcity, stochasticity, and volatility; (ii) traditional mean‐value equivalence approach performs poorly in volatile intermodal context; (iii) mean‐value‐based forecast may outperform stationary distribution‐based forecast. Our work enriches revenue management models and applications. It advances our understanding on when and how to use dynamic forecasting in intermodal revenue management.     

Customer Behavior Modeling in Revenue Management and Auctions: A Review and New Research Opportunities

Customer behavior modeling has been gaining increasing attention in the operations management community. In this paper we review current models of customer behavior in the revenue management and auction literatures and suggest several future research directions.     

基于需求更新的民航收入管理动态存量控制模型

本文对民航收入管理存量控制研究中具有里程碑意义的EMSR(Expected Marginal Seat Revenue)模型进行了评述,分析其存在的缺陷,提出将销售过程中获取的最新销售信息与需求的历史先验分布相结合,运用二维正态分布下的贝叶斯模型对需求分布进行更新,并将综合考虑新的需求预测、No-Show和取消订票等因素得到的新的需求限制与座位总数C相比较,给出更为通用的、市场反应更为灵敏的民航收入管理动态存量控制模型。     

Tractable Consideration Set Structures for Assortment Optimization and Network Revenue Management

Discrete‐choice models are widely used to model consumer purchase behavior in assortment optimization and revenue management. In many applications, each customer segment is associated with a consideration set that represents the set of products that customers in this segment consider for purchase. The firm has to make a decision on what assortment to offer at each point in time without the ability to identify the customer's segment. A linear program called the Choice‐based Deterministic Linear Program (CDLP) has been proposed to determine these offer sets. Unfortunately, its size grows exponentially in the number of products and it is NP‐hard to solve when the consideration sets of the segments overlap. The Segment‐based Deterministic Concave Program with some additional consistency equalities (SDCP+) is an approximation of CDLP that provides an upper bound on CDLP's optimal objective value. SDCP+ can be solved in a fraction of the time required to solve CDLP and often achieves the same optimal objective value. This raises the question under what conditions can one guarantee equivalence of CDLP and SDCP+. In this study, we obtain a structural result to this end, namely that if the segment consideration sets overlap with a certain tree structure or if they are fully nested, CDLP can be equivalently replaced with SDCP+. We give a number of examples from the literature where this tree structure arises naturally in modeling customer behavior.