A Newsvendor Who Chooses Informational Effort

We study a newsvendor who can acquire the services of a forecaster, or, more generally, an information gatherer (IG) to improve his information about demand. When the IG's effort increases, does the average ex ante order quantity rise or fall? Do average ex post sales rise or fall? Improvements in information technology and in the services offered by forecasters provide motivation for the study of these questions. Much depends on our model of the IG and his efforts. We study an IG who sends a signal to a classic single‐period newsvendor. The signal defines the newsvendor's posterior probability distribution on the possible demands and the newsvendor uses that posterior to calculate the optimal order. Each of the possible posteriors is a scale/location transform of the same base distribution. When the IG works harder, the average scale parameter drops. Higher IG effort is always useful to the newsvendor. We show that there is a critical value of order cost. For costs on one side of this value more IG effort leads to a higher average ex ante order and for costs on the other side to a lower average order. But for all costs, more IG effort leads to higher average ex post sales. We obtain analogous results for a “regret‐averse” newsvendor who suffers a penalty that is a nonlinear function of the discrepancy between quantity ordered and true demand.     

Responsive Pricing Newsvendor Networks with Discretionary Commonality

Discretionary commonality is a form of operational flexibility used in multi‐product manufacturing environments. Consider a case where a firm produces and sells two products. Without discretionary commonality, each product is made through a unique combination of input and production capacity. With discretionary commonality, one of the inputs could be used for producing both products, and one of the production capacities could be used to process different inputs for producing one of the products. In the latter case, the manager can decide, upon the realization of uncertainty, not only the quantities for different products (outputs) but also the means of transforming inputs into outputs. The objective of this study is to understand how the firm's value, its inventory levels for inputs and capacity levels for resources are affected by the demand characteristics and market conditions. In pursuing this research, we extend Van Mieghem and Rudi ( 2002 )'s newsvendor network model to allow for the modeling of product interdependence, demand functions, random shocks, and firm's ex post pricing decision. Applying the general framework to the network with discretionary commonality, we discover that inventory and capacity management can be quite different compared to a network where commonality is non‐discretionary. Among other results, we find that as the degree of product substitution increases, the relative need for discretionary commonality increases; as the market correlation increases, while the firm's value may increase for complementary products, the discretionary common input decreases but the dedicated input increases. Numerical study shows that discretionary flexibility and responsive pricing are strategic substitutes.     

Advance Selling by a Newsvendor Retailer

Retailers often face a newsvendor problem. Advance selling helps retailers to reduce demand uncertainty. Consumers, however, may prefer not to purchase in advance unless given a discount because they are uncertain about their valuation for the product in advance. It is then unclear whether or when advance selling to pass some uncertainty risk to consumers is optimal for the retailer. This paper examines the advance selling price and inventory decisions in a two‐period setting, where the first period is the advance selling period and the second is the selling (and consumption) period. We find that an advance selling strategy is not always optimal, but is contingent on parameters of the market (e.g., market potential and uncertainty) and the consumers (e.g., valuation, risk aversion, and heterogeneity). For example, we find that retailers should sell in advance if the consumers' expected valuation exceeds consumers' expected surplus when not buying early by a certain threshold. This threshold increases with the degree of risk aversion but decreases with stock out risk. If the degree of risk aversion varies across consumers, then a retailer should sell in advance if the probability for a consumer to spot buy is less than a critical fractile.     

The Newsvendor Problem and Price‐Only Contract When Bankruptcy Costs Exist

We study a supply chain of a supplier selling via a wholesale price contract to a financially constrained retailer who faces stochastic demand. The retailer might need to borrow money from a bank to execute his order. The bank offers a fairly priced loan for relevant risks. Failure of loan repayment leads to a costly bankruptcy (fixed administrative costs, costs proportional to sales, and a depressed collateral value). We identify the retailer's optimal order quantity as a function of the wholesale price and his total wealth (working capital and collateral). The analysis of the supplier's optimal wholesale price problem as a Stackelberg game, with the supplier the leader and the retailer the follower, leads to unique equilibrium solutions in wholesale price and order quantity, with the equilibrium order quantity smaller than the traditional newsvendor one. Furthermore, in the presence of the retailer's bankruptcy risks, increases in the retailer's wealth lead to increased supplier's wholesale prices, but without the retailer's bankruptcy risks the supplier's wholesale prices stay the same or decrease in retailer's wealth.     

带有马尔可夫竞争因子的多产品报童模型

在竞争的环境下考虑多产品报童问题。为了刻画多产品间的竞争关系，本文利用马尔可夫链构建多产品的需求转移模型，并根据模型的转移概率矩阵提出马氏竞争因子和综合竞争力等核心概念，进而结合卷积公式和雅可比行列式，将竞争因子的概念纳入经典报童模型的框架，构建了带有马氏竞争因子的多产品报童模型，同时在该模型的理论基础上给出了新的决策机制。模型的数据实验表明：竞争因子对多产品库存系统的最优订购策略具有重要的影响，关于产品的综合竞争力为单调递增函数；将竞争因子纳入多产品库存系统的决策机制，可进一步拓展报童模型在实际应用领域中的适应性以及提高库存系统的优化与控制的效用。     

Newsvendor Pricing Problem in a Two‐Sided Market

We study the pricing problem of a “platform” intermediary to jointly determine the selling price of the platforms (hardware) sold to consumers and the royalty charged to content developers for content (software), when the demands for content and for platforms are interdependent. Our model elucidates the impact of supply chain replenishment costs and demand uncertainty on the strategic issues of platform pricing in a two‐sided market.     

需求分布规律变化情况下的报童订货策略

在需求分布规律变化情况下,报童在进行订货决策时会因为错误判断需求分布规律而导致期望库存成本增加。为了解决这一问题,本文集成传统历史需求信息和非传统需求信息以正确地认知需求分布规律,在此基础上决策订货量。假设需求服从均值不同、方差相同的两种类型的正态分布,每一种正态分布的概率已知。利用信号检测理论构建基于历史需求信息与需求分布概率的报童最优订货策略,并与只基于需求分布概率的直觉规则订货策略进行对比。结果表明：只要排除需求分布概率很大或很小两种极端情况,最优订货策略比直觉规则订货策略在控制期望库存成本方面的作用更明显,即利用历史需求信息可以有效修正报童对实际需求分布的检测结果,从而提高实际订货决策的准确性。研究结果对传统历史需求信息和非传统需求信息的集成以及需求信息交换等有一定的管理学启示和应用价值。     

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。     

On the Unimodality of the Profit Function of the Pricing Newsvendor

In this note, we study the price‐setting newsvendor problem. We use three conditions, the log‐convexity of the coefficient of variation, the log‐concavity of the deterministic profit function, and the log‐convexity of the random noise's expectation conditional on having leftover inventory to establish the log‐concavity of the retailer's expected profit function. This new result is complementary to existing results and removes some assumptions in the pricing and inventory coordination literature. It also addresses the conjecture made by Petruzzi and Dada (1999), and can be applied in the pricing game.     

Signaling to Partially Informed Investors in the Newsvendor Model

We analyze a signaling game between the manager of a firm and an investor in the firm. The manager has private information about the firm's demand and cares about the short‐term stock price assigned by the investor. Previous research has shown that under continuous decision choices and the Intuitive Criterion refinement, the least‐cost separating equilibrium will result, in which a low‐quality firm chooses its optimal capacity and a high‐quality firm over‐invests in order to signal its quality to investors. We build on this research by showing the existence of pooling outcomes in which low‐quality firms over‐invest and high‐quality firms under‐invest so as to provide identical signals to investors. The pooling equilibrium is practically appealing because it yields a Pareto improvement compared to the least‐cost separating equilibrium. Distinguishing features of our analysis are that: (i) we allow the capacity decision to have either discrete or continuous support, and (ii) we allow beliefs to be refined based on either the Undefeated refinement or the Intuitive Criterion refinement. We find that the newsvendor model parameters impact the likelihood of a pooling outcome, and this impact changes in both sign and magnitude depending on which refinement is used.     

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.     

基于预期的报童问题研究

Koszegi与Rabin认为参照点往往由决策者的理性预期确定,本文选取报童的预期作为参照点,利用参照依赖偏好理论对报童问题进行了研究。研究发现,基于预期的报童的最优订货量不仅与货物销售的概率分布、价格等有关还与报童的损失厌恶程度有关。如果报童是损失厌恶的,报童的订货量要小于经典报童问题的订货量;反之,报童的订货量则大于经典报童问题的订货量,该结论与大部分实证结果是一致的。最后,用算例来验证了文中有关结论的正确性。     

Optimal Pricing,Ordering, and Return Policies for Consumer Goods

Our research addresses a firm that sells a product to consumers who are sensitive to both price and return policy. The operational decisions of interest are the selling price, return policy, and quantity of new product to purchase. We model a single selling season that is split into two periods where the boundary between periods is delineated by the opportunity to recover product returns and resell them. That is, returns in the first period can be recovered and sold in the second period. Returns also arise in the second period, but these may only be salvaged. We first analyze both deterministic and stochastic models, finding that the deterministic results largely carry over to the stochastic case. In addition, our results indicate that the model is quite insensitive to errors in the estimates of the parameter values, except for purchase cost and parameters related to demand. Finally, we perform an analysis on the value of various investments to improve financial performance. Results indicate that investments to reduce the recovery cost of returns or reduce returns uncertainty are minimal, while investments to increase recovery speed, reduce market uncertainty, and reduce the return rate can be quite valuable.     

The Dynamic Newsvendor Model with Correlated Demand

The classic newsvendor model was developed under the assumption that period‐to‐period demand is independent over time. In real‐life applications, the notion of independent demand is often challenged. In this article, we examine the newsvendor model in the presence of correlated demands. Specifically under a stationary AR(1) demand, we study the performance of the traditional newsvendor implementation versus a dynamic forecast‐based implementation. We demonstrate theoretically that implementing a minimum mean square error (MSE) forecast model will always have improved performance relative to the traditional implementation in terms of cost savings. In light of the widespread usage of all‐purpose models like the moving‐average method and exponential smoothing method, we compare the performance of these popular alternative forecasting methods against both the MSE‐optimal implementation and the traditional newsvendor implementation. If only alternative forecasting methods are being considered, we find that under certain conditions it is best to ignore the correlation and opt out of forecasting and to simply implement the traditional newsvendor model.      

Using Contingent Markdown with Reservation to Profit from Strategic Consumer Behavior

We examine a contingent price markdown (CM) mechanism with guaranteed reservation under which a retailer sells multiple units to forward‐looking consumers who arrive over time according to a Poisson process. During the early part of the selling season, each arriving consumer can either purchase a unit by paying the regular price or reserve a unit at the discount price. Reserved units can only be claimed later when the number of guaranteed reservations meets a pre‐specified threshold, or at the end of the selling season, whichever comes first. Immediately after the number of guaranteed reservations meets the pre‐specified threshold, the retailer will reduce its selling price to the discount price so that all subsequent arriving consumers can take immediate possession by paying the low price. We study the consumer purchasing behavior in equilibrium when the retailer adopts such a selling mechanism, and compare the performance of our mechanism against two benchmarks: fixed price (FP) and pre‐announced discount (PD). Through an extensive numerical analysis, we identify market conditions under which CM dominates both FP and PD in terms of the retailer's revenue and consumer's surplus. Finally, through a fluid approximation to the stochastic model, we simplify the computation of the equilibrium strategy and the optimal revenues, and verify that the key insights obtained from the stochastic model still hold.     

Design for the Environment: Life‐Cycle Approach Using a Newsvendor Model

Introducing environmental innovations in product and process design can affect the product's cost and demand, as well as the environmental impact in different stages of its life cycle (such as manufacturing and use stages). In this article, we advance understanding on where such design changes can be most effective economically to the firm and examine their corresponding environmental consequences. We consider a profit maximizing firm (newsvendor) deciding on the production quantity as well as its environmentally focused design efforts. We focus our results along the two dimensions of demand characteristics and life‐cycle environmental impact levels, specifically functional vs. innovative products, and higher manufacturing stage environmental impact vs. higher use stage environmental impact. We also discuss the environmental impact of overproduction and how it relates to the different types of products and their salvage options. We find that although the environmental impact per unit always improves when firms use eco‐efficient or demand‐enhancing innovations, the total environmental impact can either increase or decrease due to increased production quantities. We identify the conditions for such cases by looking at the environmentally focused design efforts needed to compensate for the increase in production. We also show that the environmental impact of overproduction plays an important role in the overall environmental impact of the firm. We conclude by applying our model to different product categories.     

Ordering,Pricing, and Lead‐Time Quotation Under Lead‐Time and Demand Uncertainty

In this article, we study the newsvendor problem with endogenous setting of price and quoted lead‐time. This problem can be observed in situations where a firm orders semi‐finished product prior to the selling season and customizes the product in response to customer orders during the selling season. The total demand during the selling season and the lead‐time required for customization are uncertain. The demand for the product depends not only on the selling price but also on the quoted lead‐time. To set the quoted lead‐time, the firm has to carefully balance the benefit of increasing demand as the quoted lead‐time is reduced against the cost of increased tardiness. Our model enables the firm to determine the optimal selling price, quoted lead‐time, and order quantity simultaneously, and provides a new set of insights to managers.     

考虑策略性消费者的生鲜农产品定价和库存决策

消费者的策略性行为使零售商的生鲜农产品的定价和库存决策面临更大挑战。本文基于报童模型,综合考虑消费者的策略性行为,对生鲜农产品价值下降进行离散化处理。刻画策略性消费者的决策行为,构建零售商的单阶段和两阶段定价及库存决策模型,分析了产品价值剩余率对消费者行为、零售商最优定价、最优库存水平以及零售商利润的影响机理。研究发现,在单阶段模型中零售商最优价格和最优库存水平均随产品价值剩余率的递增而递增;而在两阶段模型中,第二阶段最优价格随价值剩余率的变化趋势可能存在阈值。     

Modeling Strategic Behavior in The Competitive Newsvendor Problem: An Experimental Investigation

This study experimentally investigates ordering behavior in the competitive newsvendor problem. We consider a duopoly market setting with two identical newsvendors selling the same perishable goods in a common market. Our experimental results show that average observed orders systematically deviate from the Nash equilibrium, and exhibit a similar pull‐to‐center pattern as in the classic non‐competitive newsvendor experiments: average orders fall below the Nash equilibrium in the high‐margin condition, and above the Nash equilibrium in the low‐margin condition. More importantly, the observed orders in the duopoly market are significantly higher than that in the non‐competitive newsvendor market, even in situations where standard inventory models predict no difference. We explain the ordering behavior using a strategic experience‐weighted attraction (EWA) model, which captures players' propensities for strategic thinking in game settings. Our empirical analysis suggests that the strategic EWA model generates more accurate predictions of future ordering behavior than an existing linear adaptive model without concerning strategic thinking. Further analysis shows that individuals are heterogeneous in their propensities to be a strategic player. Our research indicates the importance of modeling strategic behavior when analyzing behavioral decisions in competitive (game) environments.     

How Costs and Heterogeneous Consumer Price Sensitivity Interact with Add‐On Pricing

Firms often cite cost savings as a reason why they charge separately for add‐ons. Firms also often face situations where consumers' price sensitivity is correlated with their valuation of add‐ons. While cost savings may directly translate into profit gains in some scenarios, this study examines the strategic implications of add‐on pricing and is the first to suggest that cost savings from add‐on pricing may in fact result in profit loss for firms when consumers are heterogeneous in price sensitivity. This is because add‐on pricing can trigger a revenue loss that exceeds any cost savings, thus leading to a negative net profit change for competing firms. Even if firms have the capability to pre‐commit to not adopting add‐on pricing, we show that competing firms can be locked in a prisoner's dilemma where all choose to adopt add‐on pricing and lose profits (as compared to none adopting add‐on pricing). We further show the possibility that the greater the cost of providing the add‐on (and the greater the cost savings generated from add‐on pricing), the worse this profit loss gets.