基于策略消费者行为和市场细分的联合定价库存策略

策略消费者的行为越来越受到厂商的重视,本文在假设消费者为风险规避型,对商品评价异质,考虑策略消费者和非策略消费者并存的细分市场上,比较两阶段定价和单一定价的优劣,研究限量策略实施的条件,进一步扩展至厂商能同时决定库存和价格的情况。研究表明消费者为风险规避型时,两阶段定价策略优于单一定价策略;策略消费者所占比例越大,消费者风险规避程度越高,第二阶段价格折扣越大,厂商越青睐限量的两阶段定价策略。此外,制定适度的价格折扣才会使厂商增加利润,过度的折扣竞争对厂商和消费者都没有好处。     

Managing Clearance Sales in the Presence of Strategic Customers

We study the effect of strategic customer behavior on pricing and rationing decisions of a firm selling a single product over two periods. The seller may limit the availability of the product (that is, ration) in the second (clearance) period. Some customers are strategic and respond to the firm's decisions by timing their purchases. When capacity is nonconstraining and the seller has pricing flexibility, we show that rationing in the clearance period cannot improve revenue. However, when prices are fixed in advance, rationing can improve revenue. In the latter case, we conduct a detailed analysis for linear and exponential demand curves and derive explicit expressions for optimal rationing levels. We find that the policy of doing the better of not restricting availability at the clearance price or not offering the product at the clearance price is typically near optimal. Our analysis also suggests that rationing—although sometimes offering considerable benefit over allowing unrestricted availability in the clearance period—may allow the seller to obtain only a small fraction of the optimal revenue when the prices are chosen optimally without rationing. We extend the analysis to cases where the capacity is constraining and obtain similar results.     

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.     

UNCERTAIN DEMAND,CONSUMER LOSS AVERSION,AND FLAT‐RATE TARIFFS

We consider a model of firm pricing and consumer choice, where consumers are loss averse and uncertain about their future demand. Possibly, consumers in our model prefer a flat rate to a measured tariff, even though this choice does not minimize their expected billing amount—a behavior in line with ample empirical evidence. We solve for the profit‐maximizing two‐part tariff, which is a flat rate if (a) marginal costs are not too high, (b) loss aversion is intense, and (c) there are strong variations in demand. Moreover, we analyze the optimal nonlinear tariff. This tariff has a large flat part when a flat rate is optimal among the class of two‐part tariffs.     

考虑零售商失望规避与欣喜寻求的定价与订货联合决策

现实中,零售商在定价与订货联合决策中往往会关注实际收益与预期收益的差异,并表现出失望规避与欣喜寻求行为,而针对考虑零售商失望规避与欣喜寻求行为的定价与订货联合决策问题的研究成果还不多见。在本文中,首先依据失望理论刻画了基于零售商预期收益的失望-欣喜效用函数,并在此基础上构建了考虑零售商失望-欣喜效用的定价与订货联合决策效用函数;然后,通过分析确定了使期望效用最大化的最优零售价格与最优订货量;进一步地,通过数值实验分析了零售商不同的预期收益、失望规避程度与欣喜寻求程度对其最优零售价格与最优订货量的影响。研究结果表明,零售商不同的预期收益以及失望规避程度与欣喜寻求程度均能够影响定价与订货联合决策结果,且针对具有不同预期收益的零售商,其失望规避程度与欣喜寻求程度对其最优决策结果的影响不同。     

引入策略型消费者遗憾心理的时尚产品定价策略

通过对时尚策略型消费行为的研究,把消费者心理动机归结为两种,其一是因冲动购买而错过降价产生的“高价遗憾”;其二是因等待降价并延迟购买而遭遇缺货产生的“缺货遗憾”,并在此基础上,在一个两周期销售中分析其对企业的降低标价(Markdown, MD)与抬高标价(Markup, MU)两种定价模式的影响机理。首先把两种遗憾心理因素纳入消费者的效用函数,建模分析了需求随机下降低标价(抬高标价)两阶段销售模式中供应商如何通过考虑消费者行为设置不同阶段价格和限量配给水平的决策。并在此基础上通过不同定价模式下供应商收益参数的对比,重点分析了两种遗憾心理因素效应对销售阶段分割的综合影响。研究发现：有遗憾心理的消费者将削弱延迟购买倾向,供应商可通过制造适当的配给风险诱导顾客高价期购买;其次两种定价类型下,当满足一定条件时,面对遗憾心理的消费群体,企业均能实现比统一定价更高的最优收益,并且抬高标价比降低标价的优化效果更明显。     

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。     

The Promise of Strategic Customer Behavior: On the Value of Click Tracking

Click tracking is gaining in popularity, and the practice of web analytics is growing fast. Whether strategic customers are willing to visit a website when they know their clicks may be tracked is an important yet complex problem, which depends on various factors. Using a newsvendor framework, we examine this problem by focusing on the operational factor: how product availability induces strategic customers to voluntarily provide advance demand information. We find that a strong Nash equilibrium exists where every customer is willing to click, and customer incentives to click are robust to noise. Hence, we demonstrate the promise of strategic customer behavior in the context of click tracking, contrary to the conventional wisdom that it is typically a peril for the firm. Notably, click tracking is typically advantageous to both the firm and its customers, compared with other strategies such as advance selling, quantity commitment, availability guarantees, and quick response. Lastly, we extend to two settings by including marketing decisions, price‐sensitive demand and markdown pricing, and discuss how operations and marketing decisions interact in influencing the value of click tracking.     

Ambiguity,Learning, and Asset Returns

We propose a novel generalized recursive smooth ambiguity model which permits a three‐way separation among risk aversion, ambiguity aversion, and intertemporal substitution. We apply this utility model to a consumption‐based asset‐pricing model in which consumption and dividends follow hidden Markov regime‐switching processes. Our calibrated model can match the mean equity premium, the mean risk‐free rate, and the volatility of the equity premium observed in the data. In addition, our model can generate a variety of dynamic asset‐pricing phenomena, including the procyclical variation of price–dividend ratios, the countercyclical variation of equity premia and equity volatility, the leverage effect, and the mean reversion of excess returns. The key intuition is that an ambiguity‐averse agent behaves pessimistically by attaching more weight to the pricing kernel in bad times when his continuation values are low.     

Technical Note – Pricing Below Cost Under Exchange‐Rate Risk

Pricing below cost is often classified as “dumping” in international trade and as “predatory pricing” in local markets. It is legally prohibited from practice because of earlier findings that it leads to predatory behavior by either eliminating competition or stealing market share. This study shows that a stochastic exchange rate can create incentives for a profit‐minded monopoly firm to set price below marginal cost. Our result departs from earlier findings because the optimal pricing decision is based on a rational behavior that does not exhibit any malicious intent against the competition to be considered as violating anti‐trust laws. The finding is a robust result, because our analysis demonstrates that this behavior occurs under various settings such as when the firm (i) is risk‐averse, (ii) can postpone prices until after exchange rates are realized, (iii) is capable of manufacturing in multiple countries, and (iv) operates under demand uncertainty in addition to the random exchange rate.     

A Model of Consumer Inertia with Applications to Dynamic Pricing

This paper introduces a decision model of consumer inertia. Consumers exhibit inertia when they have an inherent bias to delay purchases. Inertia may induce consumers to wait even when it is optimal to buy immediately. We embed our decision model within a dynamic pricing context. There is a firm that sells a fixed capacity over two time periods to an uncertain number of both rational and inertial consumers. We find that consumer inertia has both positive and negative effects on profits: it decreases demand (in period one) but intensifies competition among consumers for the product (in period two). We show that our model of inertia is consistent with well‐established behavioral regularities, such as loss aversion and probability weighting in the sense of prospect theory, and hyperbolic time preferences. We offer practical recommendations for firms to influence the level of consumer inertia. These include offering returns policies (to mitigate potential consumer losses), providing decision aids (to avoid perception errors), and offering flexible payment options (to lower transaction costs).     

Capacity Planning with Financial and Operational Hedging in Low‐Cost Countries

The authors of this article outline a capacity planning problem in which a risk‐averse firm reserves capacities with potential suppliers that are located in multiple low‐cost countries. While demand is uncertain, the firm also faces multi‐country foreign currency exposures. This study develops a mean‐variance model that maximizes the firm's optimal utility and derives optimal utility and optimal decisions in capacity and financial hedging size. The authors show that when demand and exchange rate risks are perfectly correlated, a risk‐averse firm, by using financial hedging, will achieve the same optimal utility as a risk‐neutral firm. In this study as well, a special case is examined regarding two suppliers in China and Vietnam. The results show that if a single supplier is contracted, financial hedging most benefits the highly risk‐averse firm when the demand and exchange rate are highly negatively related. When only one hedge is used, financial hedging dominates operational hedging only when the firm is very risk averse and the correlation between the two exchange rates have become positive. With both theoretical and numerical results, this study concludes that the two hedges are strategic tools and interact each other to maximize the optimal utility.     

风险规避与企业的产生和发展

本文沿阿尔钦的风险规避(risk aversion)思想继续深入,认为企业的产生和发展是根源于所有参与人的风险规避动机,修正了新古典经济学的关于企业、企业家和资本家的风险中性和风险偏好假设,使理性经济人假设保持一致,并证明风险规避动机促使企业产生和发展,最后还以企业产生的历史、今天的发展和企业的存在形式作为分析验证的佐证。其中关于风险的证明在金融经济学、资产定价模型理论中具有广泛的应用。     

存在战略购买需求的定价、供给、机制选择和配给研究

本文研究存在战略购买需求的易逝资产销售策略问题。垄断厂商基于利润最大化目标确定易逝资产定价、供给、机制选择和配给策略,战略消费者通过锚定预期价格安排战略购买时机。不同于通常基于效用理论研究定价的思路,本文首先基于锚定效应和跨期价格均衡思想探寻不同战略等待购买规模的市场预期需求曲线和动静态定价区域;其次在众多预期需求曲线中寻找市场有效定价前沿（即有效预期需求曲线）;再次在利润曲面上找出与有效定价前沿对应的容量扩展线（即最大利润曲线）;最后沿容量扩展线和有效定价前沿搜寻最大期望利润及相应策略。研究表明,消费者保留价异质和需求不确定性是动态定价和战略购买存在的根本原因;市场在不同战略等待购买规模状态拥有不同预期需求曲线,最大战略等待购买规模状态预期需求曲线是市场有效定价前沿。动静态定价机制各有其所适用的容量和价格空间,消费者保留价水平和战略消费者规模决定动态定价空间大小,随机需求分布差异只影响动态定价空间形状（即影响需求弹性）。在跨期价格均衡区域内,提价和扩容都会加剧消费者战略购买程度,供给越大定价往往越低。战略购买不仅会降低厂商供给、定价和利润水平,改变不同类型消费者之间高低价购买机会,甚至还可能影响定价机制选择和配给策略。压缩过度供给和虚高价格空间可降低战略购买导致的利润损失。本文研究结果可为考虑消费者行为的需求价格理论研究和运营管理实践提供参考。     

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.     

INVENTORY RATIONING AND SHIPMENT FLEXIBILITY ALTERNATIVES FOR DIRECT MARKET FIRMS

This paper investigates inventory‐rationing policies of interest to firms operating in a direct market channel. We model a single product with two demand classes, where one class requests a lower order fulfillment lead time but pays a higher price. Demand for each class follows a Poisson process. Inventory is fed by a production system with exponentially distributed build times. We study rationing policies in which the firm either blocks or backlogs orders for the lower priority customers when inventory drops below a certain level. We compare the performance of these rationing policies with a pure first‐come, first‐serve policy under various scenarios for customer response to delay: lost sales, backlog, and a combination of lost sales and backlog.     

Optimal Temporal Customer Purchasing Decisions Under Trade‐In Programs with Up‐Front Fees

To entice customers to purchase both current and new generation products over time, many firms offer different trade‐in programs including programs that require customers to pay an up‐front fee. To examine the effectiveness of the trade‐in programs, we develop a two‐period model in which a firm sells the first generation product in the first period and the second generation product in the second period; however, the firm offers a trade‐in program that customers can participate in when purchasing the first generation product in the first period. To participate, each customer has to pay a nonrefundable fee in the first period so that she has the option to trade‐in her first generation product and receive a prespecified trade‐in value to be used for the purchase of the second generation product in the second period. To capture market heterogeneity and market uncertainty, we examine the case when the valuation of the first generation product varies among customers and the valuation of the second generation product is uncertain a priori. By analyzing a two‐period game, we determine the optimal purchasing behavior of each rational customer, and we show that the firm is always better off by offering its own trade‐in programs. Also, our numerical analysis reveals that trade‐in programs can benefit the firm significantly especially when (i) the residual value of the first generation product is high; (ii) the expected incremental value of the second generation product is high; or (iii) the valuation of the second generation product is highly uncertain.     

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。     

需求学习下考虑顾客策略行为的供应链决策

顾客策略行为对企业的经营绩效带来了巨大的负面影响, 本文基于供应链背景, 探讨需求学习应对顾客策略行为的作用与价值。构建了由单一制造商、单一零售商和一组顾客群组成的两周期分散式供应链系统的博弈模型, 将顾客划分为短视型和策略型两种类型。采用数理模型和数值分析, 研究了需求学习对于供应链的定价决策、订货决策及整体绩效的影响, 得到如下主要研究结论:第一, 无论面对何种类型的顾客, 零售商均偏好需求学习获取需求更新信息;第二, 面对短视顾客时, 制造商偏好于不获取更新信息, 而当顾客为策略型时, 制造商偏好于获取更新信息;第三, 需求学习有助于提高零售商和供应链系统的利润, 特别当面对策略型顾客时, 需求学习带来的利润增值更大。以上研究结论表明, 需求学习可以有效地缓解顾客策略行为的负面影响, 提高企业的运营绩效。     

基于异质性顾客的随机配给策略研究

文中考虑了三类异质顾客:战略顾客、迟钝顾客与询价顾客,其中,战略顾客具有完全理性与风险中性特征;迟钝顾客由于其迟钝本性,表现出有限理性与隐性风险规避特征,这两类顾客的战略等待加剧了产品供给与需求的不匹配风险。研究了销售商采用随机配给策略以减少延迟购买期中产品可获得概率,促使战略顾客与迟钝顾客提前购买的价值。结论表明,在固定折扣价格策略中,当迟钝顾客的迟钝强度较低时,销售商最优策略是故意创造配给风险分割市场;在弹性折扣价格策略中,销售商是否运用随机配给策略不仅与迟钝强度有关,还取决于弹性价格折扣幅度。然后运用数值分析对这两种机制进行了比较,发现,销售商采用弹性折扣价格策略时,弹性折扣价格越低,随机配给的价值越大,即提供较大幅度价格折扣,反而增加其利润。