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。     

Impact of Price Postponement on Capacity and Flexibility Investment Decisions

Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made.     

Pricing and Capacity Rationing with Customer Disappointment Aversion

Customers are averse to disappointment that arises when economic outcomes fall short of expectations. In this study, we study a two‐period model in which the firm may create rationing in either period. In the anticipation of possible disappointment due to stock‐outs, strategic customers decide when to purchase and the firm determines the prices and rationing levels in each period. We explore the impact of disappointment aversion on customers' strategic purchasing behavior and the firm's pricing and rationing decisions. Without disappointment aversion, it is optimal for the firm to adopt a uniform pricing policy without rationing. However, when strategic customers are averse to disappointment, a firm may be able to increase profits with an appropriate level of rationing. We analyze both the mark‐up and mark‐down policies. We show that, in a mark‐down scenario, the firm always benefits from disappointment aversion behavior by using an appropriate level of rationing in a low‐price period. However, in a mark‐up scenario, whether it is beneficial for the firm to induce disappointment aversion behavior depends on how customers frame payoffs in different periods when forming utilities. Particularly, when customers compartmentalize payoffs in different periods to form utilities, the firm should not induce disappointment aversion behavior.     

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.     

Advance selling with freebies and limited production capacity

We consider a two-period pricing model in which a seller offers freebies along with the product when making advance sales, and production is constrained by capacity. The seller can offer freebies to increase both market base and customer׳s valuation toward the product in advance. The customers strategically determine whether to purchase the product in advance and gain freebies when their valuation on the product is uncertain, or delay their purchase decision until the regular selling period. We characterize the optimal pricing, quality level of the freebie and production quantity decisions that maximize the expected profits of the seller over the two periods.     

A comparison of fixed and dynamic pricing policies in revenue management

We consider the problem of selling a fixed capacity or inventory of items over a finite selling period. Earlier research has shown that using a properly set fixed price during the selling period is asymptotically optimal as the demand potential and capacity grow large and that dynamic pricing has only a secondary effect on revenues. However, additional revenue improvements through dynamic pricing can be important in practice and need to be further explored. We suggest two simple dynamic heuristics that continuously update prices based on remaining inventory and time in the selling period. The first heuristic is based on approximating the optimal expected revenue function and the second heuristic is based on the solution of the deterministic version of the problem. We show through a numerical study that the revenue impact of using these dynamic pricing heuristics rather than fixed pricing may be substantial. In particular, the first heuristic has a consistent and remarkable performance leading to at most 0.2% gap compared to optimal dynamic pricing. We also show that the benefits of these dynamic pricing heuristics persist under a periodic setting. This is especially true for the first heuristic for which the performance is monotone in the frequency of price changes. We conclude that dynamic pricing should be considered as a more favorable option in practice.     

Approximation algorithms for pricing with negative network externalities

We study the problems of pricing an indivisible product to consumers who are embedded in a given social network. The goal is to maximize the revenue of the seller by the so-called iterative pricing that offers consumers a sequence of prices over time. The consumers are assumed to be impatient in that they buy the product as soon as the seller posts a price not greater than their valuations of the product. The product’s value for a consumer is determined by two factors: a fixed consumer-specified intrinsic value and a variable externality that is exerted from the consumer’s neighbors in a linear way. We focus on the scenario of negative externalities, which captures many interesting situations, but is much less understood in comparison with its positive externality counterpart. Assuming complete information about the network, consumers’ intrinsic values, and the negative externalities, we prove that it is NP-hard to find an optimal iterative pricing, even for unweighted tree networks with uniform intrinsic values. Complementary to the hardness result, we design a 2-approximation algorithm for general weighted networks with (possibly) nonuniform intrinsic values. We show that, as an approximation to optimal iterative pricing, single pricing works fairly well for many interesting cases, such as forests, Erd?s–Rényi networks and Barabási–Albert networks, although its worst-case performance can be arbitrarily bad in general networks.     

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.     

Coping with Gray Markets: The Impact of Market Conditions and Product Characteristics

Gray markets, also known as parallel imports, have created fierce competition for manufacturers in many industries. We analyze the impact of parallel importation on a price‐setting manufacturer that serves two markets with uncertain demand, and characterize her policy against parallel importation. We show that ignoring demand uncertainty can take a significant toll on the manufacturer's profit, highlighting the value of making price and quantity decisions jointly. We find that adjusting prices is more effective in controlling gray market activity than reducing product availability, and that parallel importation forces the manufacturer to reduce her price gap while demand uncertainty forces her to lower prices. Furthermore, we explore the impact of market conditions (such as market base, price sensitivity, and demand uncertainty) and product characteristics (“fashion” vs. “commodity”) on the manufacturer's policy towards parallel importation. We also provide managerial insights about the value of strategic decision‐making by comparing the optimal policy to the uniform pricing policy that has been adopted by some companies to eliminate gray markets entirely. The comparison indicates that the value of making price and quantity decisions strategically is highest for moderately different market conditions and non‐commodity products.     

顾客策略行为与风险偏好下供应链利润分享

考虑由1个生产商、1个销售商和具有策略行为与风险偏好的顾客群体所组成的供应链.存在顾客策略行为与风险偏好的情况下,利用理性预期均衡的相关知识,分析销售商定价与库存决策,研究供应链利润分享契约问题.研究结果表明:销售商的利润随着顾客风险偏好程度的增加而减少;为了缓解利润削减,销售商需要降低销售价格和订货量,而不是提高销售...     

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

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。     

基于收益共享契约的网络零售联合促销策略研究

网络零售业造节促销已成常态,优化网络零售平台(简称平台商)和销售商联合促销策略是一项值得深入研究的课题。本文基于收益共享契约,利用不同的博弈模型刻画入驻销售商和平台商之间三种不同的促销模式,包括由其中一方率先发起促销的模式和二者同时发起促销的模式,研究不同模式下销售商和平台商的最优促销策略。研究结论表明,在三种促销模式下,二者的最优促销策略均随着商品佣金费率的增长依次呈现三种不同的形式:从仅由销售商提供促销到联合促销再到仅由平台商提供促销。当且仅当佣金费率和商品的日常售价高于一定阈值时,销售商和平台商才会有动机开展联合促销。研究还发现,销售商和平台商在各自率先发起的联合促销模式下具备先动优势。销售商(平台商)率先发起的联合促销将更有利于对佣金费率较低(高)的商品实施。当销售商和平台商同时独立发起促销时,供应链整体促销力度最大,供应链的整体利润也最高。     

Durable goods pricing with reference price effects

A price benchmark shaped by consumers on the basis of their perception of past prices is known as a reference price. Behavioral decision research suggests that consumers are likely to be backward-looking in that they make purchase decisions based not only on the current price but also on the reference price. It is evident that the reference price effect, which has significant impact on consumer demand, exists for both consumables and durables. Yet, how this effect works has only been investigated in relation to the pricing of consumables, and thus the corresponding results are unable to yield normative implications for durable goods pricing where the saturation effect must enter the picture. This study aims to provide marketers of durables with relevant insights that can be practically used to guide their design of pricing strategies in the presence of the reference price effect. Specifically, we develop a dynamic pricing model which incorporates both the reference price effect and the saturation effect into a framework to broaden our understanding on the durable goods pricing problem. As the internet technology and social media have enhanced consumers’ ability to recall and compare past prices, the need for such a pricing model with backward-looking consumer behavior is increasingly compelling. Our results indicate that while it is optimal for a myopic seller to adopt the skimming pricing strategy, either the price skimming strategy or the penetration strategy is optimal for a forward-looking seller, contingent on the potential market and consumers’ reference price effects.     

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

可加效用下基于消费者惰性的易逝品动态定价

本文在考虑销售商的风险规避态度和消费者惰性的情况下，研究了易逝品的动态定价策略。首先给出风险规避的销售商实施动态定价的马尔可夫决策过程，并运用MNL随机效用模型来刻画惰性消费者的购买决策，在此基础上，以风险规避销售商的期望效用最大化为目标，利用动态规划方法建立了可加效用下的易逝品动态定价模型，并探讨了消费者的惰性行为和销售商的风险规避态度对最优价格的影响。结论表明：在销售商的风险态度为风险规避的情况下，考虑消费者惰性行为的最优价格随库存水平的增加而降低，随剩余销售时间的增加而提高，消费者的惰性行为和销售商的风险规避态度对最优价格都存在负向影响，即最优价格随惰性深度的增加而降低，随惰性宽度的增加而降低，同时，销售商的风险规避态度越强烈，其制定的产品价格越低。     

Pricing Decisions During Inter‐Generational Product Transition

How should companies price products during an inter‐generational transition? High uncertainty in a new product introduction often leads to extreme cases of demand and supply mismatches. Pricing is an effective tool to either prevent or alleviate these problems. We study the optimal pricing decisions in the context of a product transition in which a new‐generation product replaces an old one. We formulate the dynamic pricing problem and derive the optimal prices for both the old and new products. Our analysis sheds light on the pattern of the optimal prices for the two products during the transition and on how product replacement, along with several other dynamics including substitution, external competition, scarcity, and inventory, affect the optimal prices. We also determine the optimal initial inventory for each product and discuss a heuristic method.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

Dynamic Pricing in the Presence of Myopic and Strategic Consumers: Theory and Experiment

We investigate retailers’ dynamic pricing decisions in a stylized two‐period setting with possible supply constraints and demand from both myopic and strategic consumers. We present an analytical model and then test its predictions in a behavioral experiment in which human subjects played the role of pricing managers. We find that the fraction of strategic consumers in the market systematically moderates the optimal pricing structure. When this fraction exceeds a certain threshold, the retailer offers relatively small late season markdowns to discourage strategic consumers from waiting and to incentivize them to buy during the early season; otherwise, the retailer offers relatively large markdowns to divert all strategic consumers to the late season, where the majority of revenue is made. Our model analyses suggest that the latter policy is optimal under fairly broad conditions. Our experiment shows that after some significant learning, aggregate behavior is able to approximate the key qualitative predictions from our model analysis, with one notable deviation: in the presence of a mixture of myopic and strategic consumers, subjects act somewhat myopically – they underprice and oversell in the main selling season, which significantly limits their ability to generate revenue in the markdown season.     

基于好评返现和差评偏好的体验型产品两阶段定价决策研究

假定产品存在发布试销期与正式销售期,在销售商不采取好评返现与采取好评返现两种情形下分别建立考虑消费者差评偏好的两阶段定价决策模型,用KT方法得到相应的最优决策和利润,给出了销售商实施好评返现的条件。基于导函数分析方法与数值仿真技术,分析了好评返现与差评偏好对产品定价、销售商利润和消费者效用的影响,证实了好评返现下消费者重视差评信息的合理性,并针对消费者、平台和销售商提出了对策。研究表明:只有产品质量中等的销售商才会采取好评返现策略,其利润随产品质量的提升而先递增后递减;好评返现提高了销售商第二阶段的市场份额和售价,导致消费者效用损失;消费者越重视差评信息,实施好评返现的高(低)质量产品销售商越多(少),且销售商利润将下降;好评返现扭曲了评价信息的真实性,降低了消费者对在线评价系统的信任度。