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.     

多类顾客环境下报童模型中库存分配策略研究

考虑一个报童模型中多类顾客的库存分配问题,将顾客按照他们愿意支付价格的高低划分为不同级别。零售商在销售期初决定产品订货量,并在销售期内决定接受或者拒绝不同顾客的需求,以最大化销售期内的期望总利润。将销售期分成大量足够小的时间单位,通过建立一个反向Bellman动态规划方程,以优化每个时间单位内的库存分配策略,并得到了零售商最优的期初订货量。通过与没有库存分配策略下零售商的期望利润进行比较,算例分析得出库存分配策略可以大幅提高零售商的利润。这主要是因为通过库存分配可以使得零售商从高端顾客中获取更多利润,同时能够减小期初的订货量,以节约采购成本和库存持有成本。     

Profitability of Service‐Level‐Based Price Differentiation with Inventory Rationing

In this paper, we study the profitability of service‐level‐based price differentiation (SLBPD) in an inventory‐rationing context. SLBPD implies that a company offers several combinations of prices and guaranteed service levels, from which customers self‐select; different customers choose different offerings because they incur different shortage costs if an order is not fulfilled immediately. We develop an analytical model for SLBPD and explore if and when such a service differentiation strategy yields higher profits than a single undifferentiated offering. The results of our analyses suggest that SLBPD is profitable only if a company faces pricing restrictions, e.g., because of competitive pressure or regulatory restrictions. We develop necessary and sufficient conditions under which a specific and relevant form of SLBPD (called “service‐level‐based upselling”) is profitable, and provide an algorithm to compute the optimal parameters of such a policy. Based on this algorithm we carry out numerical analyses that allow us to characterize the profit increment of service‐level‐based upselling. We derive managerial insights into the attractiveness of SLBPD and explain how our basic analytical framework can be extended to account for more complex practical features.     

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.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

Money in Search Equilibrium,in Competitive Equilibrium,and in Competitive Search Equilibrium

We compare three market structures for monetary economies: bargaining (search equilibrium); price taking (competitive equilibrium); and price posting (competitive search equilibrium). We also extend work on the microfoundations of money by allowing a general matching technology and entry. We study how equilibrium and the effects of policy depend on market structure. Under bargaining, trade and entry are both inefficient, and inflation implies first‐order welfare losses. Under price taking, the Friedman rule solves the first inefficiency but not the second, and inflation may actually improve welfare. Under posting, the Friedman rule yields the first best, and inflation implies second‐order welfare losses.     

Speculation in Standard Auctions with Resale

In standard auctions resale creates a role for a speculator—a bidder who is commonly known to have no use value for the good on sale. We study this issue in environments with symmetric independent private‐value bidders. For second‐price and English auctions the efficient value‐bidding equilibrium coexists with a continuum of inefficient equilibria in which the speculator wins the auction and makes positive profits. First‐price and Dutch auctions have an essentially unique equilibrium, and whether or not the speculator wins the auction and distorts the final allocation depends on the number of bidders, the value distribution, and the discount factor. Speculators do not make profits in first‐price or Dutch auctions.     

生产能力限制下价格Stackelberg博弈模型

生产能力限制条件下,同质产品市场中两企业以价格为决策变量进行Stackelberg竞争,采取有效配给规则。两企业对称情况下,生产能力较小时模型存在唯一的子博弈精炼纳什均衡,两企业销量达到自身生产能力,得到相同收益;生产能力较大时,追随企业匹配领头企业的价格,博弈存在后动优势。分析了领头企业生产能力大于追随企业的不对称情形,并给出相应均衡。算例分析表明,企业价格竞争的前提是充分大的供给能力,追随企业应在领头企业生产能力较大时进入市场。     

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。     

Fractional Price Matching Policies Arising from the Ocean Freight Service Industry

We consider a situation in which shippers (customers) can purchase ocean freight services either directly from a carrier (service provider)in advance or from the spot market just before the departure of an ocean liner. The price is known in the former case, while the spot price is uncertain ex‐ante in the latter case. Consequently, some shippers are reluctant to book directly from the carrier in advance unless the carrier is willing to “partially match” the realized spot price when it is lower than the regular price. This study is an initial attempt to examine if the carrier should bear some of the “price risk” by offering a “fractional” price matching contract that can be described as follows. The shipper pays the regular freight price in advance; however, the shipper will get a refund if the realized spot price is below the regular price, where the refund is a “fraction” of the difference between the regular price and the realized spot price. By modeling the dynamics between the carrier and the shippers as a sequential game, we show that the carrier can use the fractional price matching contract to generate a higher demand from the shippers compared to no price matching contract by increasing the “fraction” in equilibrium. However, as the carrier increases the “fraction,” the carrier should increase the regular price to compensate for bearing additional risk. By selecting the fractional price matching contract optimally, we show that the carrier can afford to offer this price matching mechanism without incurring revenue loss: the optimal fractional price matching contract is “revenue neutral.”     

认知差异对商业银行信贷配给的影响效应分析

探讨如何缓解商业银行的信贷配给,尽最大可能满足企业特别是小企业的贷款需求是一个具有很强的现实意义的研究课题。本文在以往学者的研究基础上,将银行和企业对投资项目的风险认知差异引入模型分析,研究了风险认知差异程度和信贷配给两者之间的相关性,并基于此进行仿真模拟。结果显示,信贷配给会随着局中人风险认知差异程度的扩大而恶化,因此降低银行和企业在风险项目上的认知差异可以有效的缓解信贷配给的难题,并基于此提出了如何加大对小企业贷款的相关政策建议。     

面向批量订货和多需求类的生产与库存配给

针对一个面向两个需求类的生产企业,根据客户每次订货是否可分批交货,提出了当客户订货可分割和不可分割时供应商的最优生产和库存配给策略.分析表明,供应商的最优生产控制策略可用一个取决于系统状态的基准库存水平表示,最优的库存配给策略则用一个多层的取决于状态的配给水平向量表示.随后,该结论被推广至包含任意多个需求类的生产系统.数值分析验证了文中最优策略的有效性.     

农户资源禀赋与农业产出关系研究——基于信贷配给数据的分组讨论

本文首先把信贷配给分成数量配给、交易成本配给和风险配给三类,然后利用转换回归模型实证研究了信贷配给下农户资源禀赋与农业产出的关系。研究发现,在受到信贷约束的农户中,除了受到数量配给外,还有近四分之一的农户受到交易成本配给或风险配给。受到信贷约束农户的农业产出更加依赖于农户的资源禀赋。本文建议应根据农户不同信贷配给类型采取相应政策,以解决农户所受的信贷配给约束。     

新鲜产品跨季销售中的动态库存管理策略研究

新鲜产品在跨季销售过程中不可避免地发生变质，给分销商带来较大的风险。本文基于一个两阶段决策模型来帮助分销商动态管理库存，在考虑产品质量随机变化的情形下更好地匹配供给与需求。具体来说，在采摘季节确定采购的总数量；在销售季节结合产品新鲜度的演变以及剩余库存水平的变化动态地决策每周期的销售量，以实现期望利润的最大化。我们采用动态规划模型分析销售期的库存管理决策，刻画了利润函数和最优决策的结构性质，并考察了库存量、新鲜度水平和价格等参数对最优库存决策的影响。数值实验结果表明，当产品变质风险大、需求不确定性低时，动态库存管理策略相比静态策略的利润改进效果更为显著。     

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.     

项目投资经济效益评价原理与方法研究

本文在研究项目投资经济效益的概念与基本表达式的基础上,建立了项目投资关联优化模型,并通过实证分析,证明了该模型的科学合理性。     

Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting

This paper studies a dynamic model of perfectly competitive price posting under demand uncertainty. Firms must produce output in advance. After observing aggregate sales in prior periods, firms post prices for their unsold output. In each period, the demand of a new batch of consumers is randomly activated. Existing customers who have not yet bought and then new customers arrive at the market in random order, observe the posted prices, and either purchase at the lowest available price or delay their purchase decision. We construct a sequential equilibrium in which the output produced and its allocation across consumers is efficient. Thus consumers endogenously sort themselves efficiently, with the highest valuations purchasing first. Transaction prices in each period rise continuously, as firms become more optimistic about demand, followed by a market correction. By the last period, prices are market clearing.     

ASSESSING SOCIAL COSTS OF INEFFICIENT PROCUREMENT DESIGN

This paper considers the social costs implied by inefficient allocation of contracts in a first‐price, sealed‐bid procurement auction with asymmetric bidders. We adopt a constrained (piecewise linear) strategy equilibrium concept and estimate the structural parameters of the bidders' distribution of costs. We estimate social costs defined as the predicted cost difference between the winning firm and the most efficient bidding firm. We also compare the expected procurement costs under two different auction formats. The data is collected from procurement auctions of road painting in Sweden during 1993–1999. The results indicate that the social costs of inefficient contract allocation is about 2% of total potential production cost and that an efficient second‐price auction would lower the expected procurement cost by 2.5%. (JEL: D44, H57, C15)     

房价波动、住房信贷与宏观审慎政策

金融危机表明住房信贷违约可能引发系统性风险,但现有理论研究并未将住房信贷违约风险纳入分析框架。本文通过构建包含异质性房价冲击和住房信贷违约的房地产动态随机一般均衡（DSGE）模型,探究房价波动的溢出效应,同时研究宏观审慎政策对住房信贷的监管效果。基于中国的实际数据,通过模拟分析得出以下结论：房地产市场对实体经济的溢出效应主要集中在消费而不是产出和通胀,对金融系统的溢出效应要大于实体经济。采用以住房信贷扩张速度为目标的动态资本充足率监管方式能有效地控制信贷风险,短期效果更加明显。房价波动冲击和利率冲击是引起我国住房信贷波动的主要原因。