竞争环境下基于顾客策略行为的易逝品动态定价研究

在两个提供相同易逝品的零售商折线竞争下,从顾客策略行为出发,研究竞争环境下两零售商的动态定价策略。首先建立供大于求的情况下两零售商动态定价模型,给出了均衡价格满足的条件,并探讨了在一些特殊情况下均衡价格的特性。然后将这一模型扩展到供小于求的情形,探讨模型的求解方法。算例分析了在折线竞争模式下零售商在面对顾客策略行为时,如何动态的决定价格。同时发现,在供大于求的情况下,顾客策略行为导致零售商的收益降低;在供小于求的情况下,一定程度的顾客策略行为可以使零售商获得更高的期望收益。     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

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.     

考虑战略顾客行为带预算约束的多产品报童问题

动态定价策略的广泛使用使得越来越多的顾客呈现战略性的特点,即顾客在决定购买时机时不仅会考虑当前的价格是否超过其心理预留价格,同时也会考虑到等到降价时再购买产品的可能性,从而延迟购买决策。研究了一类考虑顾客战略行为且带有预算约束的多产品报童问题,引入理性预期均衡分析,得到了报童和战略顾客双方静态博弈时的理性预计均衡解,并进一步分析了数量承诺对于均衡数量和均衡价格的影响。分析了最优解的性质并给出了求解算法,最后通过数值算例对模型的结论进行了验证。     

Quantity Competition When Most Favored Customers are Strategic

Legal studies usually treat a policy of a manufacturer or retailer as socially harmful if it reduces product output and increases the price. We consider a two‐period model where the first‐period price is fixed and resellers endogenously decide to use meet‐the‐competition clause with a most‐favored‐customer clause (MFC) to counteract strategic customer behavior. As a result of MFC, the second‐period (reduced) price increases and resellers’ inventories decrease. However, customer surplus may increase and aggregate welfare increases in the majority of market situations. MFC can mitigate the losses in welfare and resellers’ profits due to strategic customers. Moreover, under reseller competition, MFC may even lead to higher levels of these values than with myopic customers, that is, to gain from increased strategic behavior. With growing competition, benefits or losses from MFC can be higher than losses from strategic customer behavior.     

Modeling and Managing the Percentage of Satisfied Customers in Hidden and Revealed Waiting Line Systems

We perform an analysis of various queueing systems with an emphasis on estimating a single performance metric. This metric is defined to be the percentage of customers whose actual waiting time was less than their individual waiting time threshold. We label this metric the Percentage of Satisfied Customers (PSC.) This threshold is a reflection of the customers' expectation of a reasonable waiting time in the system given its current state. Cases in which no system state information is available to the customer are referred to as “hidden queues.” For such systems, the waiting time threshold is independent of the length of the waiting line, and it is randomly drawn from a distribution of threshold values for the customer population. The literature generally assumes that such thresholds are exponentially distributed. For these cases, we derive closed form expressions for our performance metric for a variety of possible service time distributions. We also relax this assumption for cases where service times are exponential and derive closed form results for a large class of threshold distributions. We analyze such queues for both single and multi‐server systems. We refer to cases in which customers may observe the length of the line as “revealed” queues.“ We perform a parallel analysis for both single and multi‐server revealed queues. The chief distinction is that for these cases, customers may develop threshold values that are dependent upon the number of customers in the system upon their arrival. The new perspective this paper brings to the modeling of the performance of waiting line systems allows us to rethink and suggest ways to enhance the effectiveness of various managerial options for improving the service quality and customer satisfaction of waiting line systems. We conclude with many useful insights on ways to improve customer satisfaction in waiting line situations that follow directly from our analysis.     

考虑顾客策略行为的易逝品定价与再制造柔性补货机制研究

本文将再制造作为一种柔性补货机制,研究了考虑顾客策略行为的易逝品定价和再制造柔性补货问题。研究表明顾客策略行为减少了零售商的期望利润,再制造柔性补货机制可以缓解顾客策略行为的影响,提高零售商的期望利润,最后分析了该机制对消费者剩余和社会福利的影响。     

基于顾客选择的酒店多房间类型联合定价研究

研究了酒店多个房间类型的客房需求存在相关性的综合定价决策问题． 首先,将所有房间类型按需求是否相关进行归类,并采用Nested Logit选择模型来刻画顾客在多房间类型多价位间的选择行为． 在考虑单天居住申请的情况下,建立了一个随机动态规划模型以描述酒店管理者的动态价格决策过程,并设计了一种求解最优定价策略的算法． 数值模拟结果表明,与不考虑各房间类型的价格决策相互影响时的情形相比,酒店多房间类型综合定价决策能获得更高的总收益和期望客房出租率,并提供更低的平均房价．     

Strategic Capacity Management When Customers Have Boundedly Rational Expectations

In retailing industries, such as apparel, sporting goods, customer electronics, and appliances, many firms deploy sophisticated modeling and optimization software to conduct dynamic pricing in response to uncertain and fluctuating market conditions. However, the possibility of markdown pricing creates an incentive for customers to strategize over the timing of their purchases. How should a retailing firm optimally account for customer behavior when making its pricing and stocking/capacity decisions? For example, is it optimal for a firm to create rationing risk by deliberately under stocking products? In this study, we develop a stylized modeling framework to answer these questions. In our model, customers strategize over the timing of their purchases. However, customers have boundedly rational expectations in the sense of anecdotal reasoning about the firm's fill rate, i.e., they have to rely on anecdotes, past experiences, or word‐of‐mouth to infer the firm's fill rate. In our modeling framework, we distinguish two settings: (i) capacity commitment, where the firm commits to its capacity level in the long run, or (ii) the firm dynamically changes it in each season. For both settings, within the simplest form of anecdotal reasoning, we prove that strategic capacity rationing is not optimal independent of customer risk preferences. Then, using a general form of anecdotal reasoning, we provide sufficient conditions for capacity rationing to be optimal for both settings, respectively. We show that the result of strategic capacity rationing being suboptimal is fairly robust to different valuation distributions and utility functions, heterogeneous sample size, and price optimization.     

基于异质性顾客心理期望等待时间的优先权服务定价研究

本文以非抢占式M/M/1排队系统为背景,以企业收益最大化为目标,基于顾客异质性(单位时间等待成本不同)将顾客分为两类,针对顾客的心理期望等待时间对服务提供商最优定价策略的影响进行研究。首先研究优先权顾客心理期望等待时间对企业收益的影响以及相应的优先权定价,然后研究优先权顾客和普通顾客同时存在心理期望等待时间对企业收益的影响和相应的优先权定价。研究表明:仅考虑优先权顾客的心理期望等待时间,企业应通过提高优先权定价来获得最优收益;当优先权顾客和普通顾客同时存在心理期望等待时间时,企业仍然采取提高优先权定价的策略,若普通顾客的价值大(获取服务的基本费用大),企业应对普通顾客提供一定的折扣来消除其心理期望等待时间增加企业收益;如果普通顾客的价值较小,企业应"有意"流失部分普通顾客,吸引更多顾客到优先权队列获取服务来获得更多收益。本文研究对于服务提供商在考虑顾客心理期望等待时间基础上设置最合理的队列机制有一定的指导意义和实际应用价值。     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

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.     

Increasing Sales by Managing the Interlocking Contingencies Between Sales Representatives and Customers Using Behavioral Self-Monitoring

Interlocking contingencies that exist between a customer and sales representatives (SRs) may contribute to buying decisions. Verbal behaviors related to closing sales were identified by analyzing these contingencies statistically. Self-observation checklists were then implemented. On average, the six targeted verbal behaviors related to sales increased 12 percentage points over baseline, compared to a 2% point increase in the comparison group. These changes were associated with 126% more sales for the experimental group compared with 36% more sales for the comparison group. For each SR, this increase in sales translates into $1,094,444 more in annualized revenue.     

Pricing in a Transportation Station with Strategic Customers

We consider a transportation station, where customers arrive according to a Poisson process, observe the delay information and the fee imposed by the administrator and decide whether to use the facility or not. A transportation facility visits the station according to a renewal process and serves all present customers at each visit. We assume that every customer maximizes her individual expected utility and the administrator is a profit maximizer. We model this situation as a two‐stage game among the customers and the administrator, where customer strategies depend on the level of delay information provided by the administrator. We consider three cases distinguished by the level of delay information: observable (the exact waiting time is announced), unobservable (no information is provided) and partially observable (the number of waiting customers is announced). In each case, we explore how the customer reward for service, the unit waiting cost, and the intervisit time distribution parameters affect the customer behavior and the fee imposed by the administrator. We then compare the three cases and show that the customers almost always prefer to know their exact waiting times whereas the administrator prefers to provide either no information or the exact waiting time depending on system parameters.     

顾客策略行为下差异产品两阶段定价模型研究

互联网和信息技术的发展,为零售商收集顾客信息带来方便的同时,也使得消费者变得越来越具有策略性和选择性。首先,构建零售商只销售一种高质量产品的情形,研究其两阶段的定价策略,并分析产品的跨期折扣因子对产品的零售价格、销售量和零售商利润的影响。然后,考虑零售商可提供高质量和低质量两种产品的情形,顾客在第一销售期、第二销售期都可以选择两种产品。构建两阶段的定价决策模型,并分析产品的跨期折扣因子、顾客对低质量产品的接受度等参数对产品两阶段的零售价格、销售量的影响。最后,用数值算例分析了第二种模型下顾客对低质量产品的接受度等模型参数对零售商两阶段总利润的影响,然后比较了第一种和第二种模型下高质量产品的零售价格和销售量。研究结论较全面的分析了顾客策略行为对差异产品两阶段销售期的定价决策的影响,为零售商进行定价优化决策提供了十分重要的参考。     

A New Dynamic Programming Decomposition Method for the Network Revenue Management Problem with Customer Choice Behavior

In this paper, we propose a new dynamic programming decomposition method for the network revenue management problem with customer choice behavior. The fundamental idea behind our dynamic programming decomposition method is to allocate the revenue associated with an itinerary among the different flight legs and to solve a single‐leg revenue management problem for each flight leg in the airline network. The novel aspect of our approach is that it chooses the revenue allocations by solving an auxiliary optimization problem that takes the probabilistic nature of the customer choices into consideration. We compare our approach with two standard benchmark methods. The first benchmark method uses a deterministic linear programming formulation. The second benchmark method is a dynamic programming decomposition idea that is similar to our approach, but it chooses the revenue allocations in an ad hoc manner. We establish that our approach provides an upper bound on the optimal total expected revenue, and this upper bound is tighter than the ones obtained by the two benchmark methods. Computational experiments indicate that our approach provides significant improvements over the performances of the benchmark methods.     

Competitive Pricing in a Multi‐Product Multi‐Attribute Environment

We address the problem of simultaneous pricing of a line of several products, both complementary products and substitutes, with a number of distinct price differentiation classes for each product (e.g., volume discounts, different distribution channels, and customer segments) in both monopolistic and oligopolistic settings. We provide a generic framework to tackle this problem, consider several families of demand models, and focus on a real‐world case‐study example. We propose an iterative relaxation algorithm, and state sufficient conditions for convergence of the algorithm. Using historical sales and price data from a retailer, we apply our solution algorithm to suggest optimal pricing, and report on numerical results.     

Managing the Revenue of Sales Platforms: Insights into Service Fees

Online sales platforms have grown substantially in recent years. These platforms assist sellers to conduct sales, and in return, collect service fees from sellers. We study the fee policies by considering a fee‐setting platform, on which a seller may conduct a sale with a reserve price to a group of potential buyers: the seller retains the object for sale if the final trading price is below the reserve price. The platform may charge two types of fees as in current practice: a reserve fee as a function of the seller's reserve price and a final value fee as a function of the sale's final trading price. We derive the optimality condition for fee policies, and show that the platform can use either just a final value fee or just a reserve fee to achieve optimality. In the former case, the optimal final value fee charged by the platform is independent of the number of buyers. In the latter case, the optimal reserve fee is often a decreasing, instead of increasing, function of the seller's reserve price. An increasing reserve fee may make the seller reluctant to use a positive reserve price and hurt the platform's revenue. In general, the optimal fees are nonlinear functions, but in reality, linear fees are commonly used because of their simplicity for implementation. We show that a linear fee policy is indeed optimal in the case that the seller's valuation follows a power distribution. In other cases, our numerical analysis suggests close‐to‐optimal performance of the linear policy.     

考虑消费者策略行为的供应链两周期定价与契约设计

针对由一个制造商与一个零售商构成的供应链,考虑消费者的策略性跨期购买行为,构建了两周期动态博弈模型,分析了消费者策略性程度对两周期均衡结果、消费者剩余和社会福利的影响,比较了分散式与集中式决策的均衡偏差,设计了与消费者策略性程度相关的两周期收益共享契约与"两周期收益共享+转移支付"组合式契约。研究表明:分散式决策下,消费者策略性程度有利于增加消费者剩余和社会福利,但会对供应链成员不利;某些情形下,消费者策略性程度会使分散式与集中式决策的系统利润差值增大;当消费者策略性程度相对较低时,两周期收益共享契约不仅可实现供应链完美协调,还可增加消费者剩余和社会福利;当消费者策略性程度较高时,通过组合式契约可实现供应链完美协调,但此时消费者策略性程度的增强可能对消费者剩余和社会福利产生负面影响。