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。     

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.     

On the benefits of operational flexibility in a distribution network with transshipment

We consider a centralized distribution network with multiple retailers who receive replenishment inventory to satisfy customer demand of the local markets. The operational flexibility of the network is defined as the opportunity that one retailer's excess inventory can be transferred to satisfy other retailers’ unmet customer demand due to stock-outs. A general modeling framework is developed to optimize retailers’ order quantities under any possible flexibility level of a stylized two-stage distribution network. We apply the framework to formulate and solve the transshipment problem of a distribution network with three retailers. Six typical flexibility levels are investigated to make the comparison study on the firm's profit performance under three ordering quantity policies: average demand, newsvendor order quantity, and optimal order quantity. We find that the operational flexibility and system optimization are complements to the firm's performance. The ordering policy with newsvendor ordering quantity can perform fairly well with moderate flexibility level when compared with the optimized ordering policy with full flexibility.     

Mean–variance analysis of the newsvendor model with stockout cost

We study the risk-averse newsvendor model with a mean–variance objective function. We show that stockout cost has a significant impact on the newsvendor's optimal ordering decisions. In particular, with stockout cost, the risk-averse newsvendor does not necessarily order less than the risk-neutral newsvendor. We illustrate this finding analytically for the case where the demand follows the power distribution.     

A Newsvendor Problem with Revenue Sharing and Channel Coordination*

Increasingly manufacturers and retailers are implementing revenue‐sharing policies to coordinate distribution channels more effectively. This article considers a standard newsvendor problem in a single manufacturer–retailer channel and compares the expected profits that each party receives in a traditional ordering environment with those that can be achieved under a revenue‐sharing policy designed to completely eliminate double marginalization. It is shown that the retailer always benefits from the transition to revenue sharing by capturing a portion of the incremental channel profit generated by the complete elimination of double marginalization. A necessary demand‐distribution‐dependent condition is derived under which the transition to revenue sharing benefits the manufacturer as well. The findings of this research are illustrated in a numerical example for the uniform demand distribution.     

The Dynamics of Domestic Gray Markets and Its Impact on Supply Chains

Gray markets are created by unauthorized retailers selling manufacturer's branded products. Similar to international gray markets, domestic gray markets are a growing phenomenon whose impact on supply chains is not clear. We consider a supply chain with one manufacturer and several authorized retailers who face a newsvendor problem and a domestic gray market. While a gray market provides an opportunity for retailers to clear their excess inventory (inventory‐correction effect), it also can be a threat to their demand (demand‐cannibalization effect). We first characterize the emerging equilibrium by assuming an MSRP environment. Comparing a decentralized and centralized system, we show that a wholesale pricing contract is quite efficient in a gray market environment; we explain the underlying mechanism and note some of the operational decisions that could hurt that efficiency. We show that the gray market price determines the degree of both the negative effects of demand‐cannibalization and the positive effects of inventory correction, which in turn determines the net impact of gray markets on the retailer's stocking choice and, ultimately, the manufacturer's profit. We then study the authorized retailers' problem as a price‐setting newsvendor. We observe that the gray market creates price competition between the authorized and unauthorized retailers, causing a drop in the primary market price. However, this price competition can be counteracted by the authorized retailers' stocking decision. Finally, we extend our model to consider the cases where the demand can be correlated across retailers.     

Decision making in the newsvendor problem: A cross-national laboratory study

In this paper, we conduct a laboratory experiment using the classic newsvendor problem to examine cross-national differences in inventory ordering patterns between Chinese and American decision makers based on a theoretical examination of the role of the Doctrine of the Mean in Chinese decision making. Drawing on the theory of context-dependent preferences (specifically extremeness aversion), we also revisit the flat-maximum hypothesis of Bolton and Katok [12], i.e., “thinning the set of order options leads to newsvendor decisions that achieve a higher proportion of maximum expected profit.” The results show that the “pull-to-center” effect is more prominent for Chinese than Americans, i.e., average order quantities of Chinese subjects are closer to the anchor of mean demand than those of American subjects. Furthermore, we find that thinning the set of order options such that the optimal order quantity is a middle option, not an extreme option in the choice set, leads to better performance in newsvendor decisions, which complements the flat-maximum hypothesis.     

Impulse Balance and Multiple‐Period Feedback in the Newsvendor Game

Human subjects in the newsvendor game place suboptimal orders: orders are typically between the expected profit‐maximizing quantity and mean demand (“pull‐to‐center bias”). In previous work, we have shown that impulse balance equilibrium (IBE), which is based on a simple ex post rationality principle along with an equilibrium condition, can predict ordering decisions in the laboratory. In this study, we extend IBE to standing orders and multiple‐period feedback and show that it predicts—in line with previous findings—that constraining newsvendors to make a standing order for a sequence of periods moves the average of submitted orders toward the optimum.     

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.      

The Newsvendor Model with Consumer Search Costs

We study the newsvendor problem when consumers are heterogeneous either in their valuations of the newsvendor's product, in their valuations of an outside option available to them, or in both valuations. In this context, we observe that the outside option, which represents the value that a given consumer associates with choosing not to purchase the newsvendor's product, may be interpreted as a search cost. Taking into consideration whether consumers' valuations differ on either one dimension of heterogeneity or on both dimensions, we develop a framework for classifying newsvendor models that incorporate demand‐management effects. In particular, we show that this framework includes both the newsvendor model with price‐dependent demand and the newsvendor model with endogenous demand as special cases. In addition to making a conceptual contribution by developing and drawing insights from this framework, we make technical contributions by providing more general sufficient conditions under which the underlying optimization problems are well behaved.     

Describing decision bias in the newsvendor problem: A prospect theory model

In the newsvendor setting, we consider a prospect theory model with a stochastic-subjective reference point. The reference point is based on the pay-offs corresponding to the extreme values of demand; and, is influenced by the perception of costs associated with understocking and overstocking, and the pessimism level of the decision maker. Our prospect theory model describes the recent observations in the newsvendor experiments—the non-linear ordering behavior with respect to the profit margin and behavior at the extreme profit margins, in addition to the pull-to-center effect and asymmetry in ordering.     

Revenue Management vs. Newsvendor Decisions: Does Behavioral Response Mirror Normative Equivalence?

We study and compare decision‐making behavior under the newsvendor and the two‐class revenue management models, in an experimental setting. We observe that, under both problems, decision makers deviate significantly from normative benchmarks. Furthermore, revenue management decisions are consistently higher compared to the newsvendor order quantities. In the face of increasing demand variability, revenue managers increase allocations; this behavior is consistent with normative patterns when the ratio of the selling prices of the two customer segments is less than 1/2, but is its exact opposite when this ratio is greater than 1/2. Newsvendors' behavior with respect to changing demand variability, on the other hand, is consistent with normative trends. We also observe that losses due to leftovers weigh more in newsvendor decisions compared to the revenue management model; we argue that overage cost is more salient in the newsvendor problem because it is perceived as a direct loss, and propose this as the driver of the differences in behavior observed under the two problems.     

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.     

Risk tolerance and a retailer's pricing and ordering policies within a newsvendor framework

This paper evaluates the pricing and ordering policies of a retailer, facing a price-dependent stochastic demand, within a newsvendor framework, under different degrees of risk tolerance and under a variety of optimizing objectives. These are (i) maximizing expected profit, for a retailer who may be risk-seeker, risk-averse or risk neutral; (ii) deriving a maximin strategy of maximizing a minimum guaranteed profit and (iii) modeling the probability of exceeding a target profit, as a constraint or as an objective. Some analytical properties and numerical examples illustrate the main features of the models and provide some comparative policy analysis across the model.     

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。     

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.     

Comparison as Incentive: Newsvendor Decisions in a Social Context

Explicit formal mechanisms dominate the discussion about incentives in Operations Management, yet many other mechanisms exist. Social comparison between peers may provide strong implicit incentives for individuals. Social comparison arises naturally in all social settings and may thus be unintended; however, many companies deliberately use it to motivate employees. In this study, we model a social context in which purchasers evaluate their performance relative to their peers; a feeling of inferiority results in a negative contribution to utility, whereas a feeling of superiority results in a positive contribution. We find that social comparison induces characteristic deviations from the newsvendor optimum ordering decision: if fear of inferiority outweighs anticipation of superiority, then purchasers herd together; the converse scenario incites actors to polarize away from each other. In both cases, actors will deviate from ordering the newsvendor optimum in order to satisfy social goals. Demand correlation and profit margins moderate the extent of the deviation.     

Myopic Analysis for Multi‐Echelon Inventory Systems with Batch Ordering and Nonstationary/Time‐Correlated Demands

We provide an exact myopic analysis for an N‐stage serial inventory system with batch ordering, linear ordering costs, and nonstationary demands under a finite planning horizon. We characterize the optimality conditions of the myopic nested batching newsvendor (NBN) policy and the myopic independent batching newsvendor (IBN) policy, which is a single‐stage approximation. We show that echelon reorder levels under the NBN policy are upper bounds of the counterparts under both the optimal policy and the IBN policy. In particular, we find that the IBN policy has bounded deviations from the optimal policy. We further extend our results to systems with martingale model of forecast evolution (MMFE) and advance demand information. Moreover, we provide a recursive computing procedure and optimality conditions for both heuristics which dramatically reduces computational complexity. We also find that the NBN problem under the MMFE faced by one stage has one more dimension for the forecast demand than the one faced by its downstream stage and that the NBN policy is optimal for systems with advance demand information and stationary problem data. Numerical studies demonstrate that the IBN policy outperforms on average the NBN policy over all tested instances when their optimality conditions are violated.     

Newsvendor Problems with Demand Shocks and Unknown Demand Distributions

In today's competitive market, demand volume and even the underlying demand distribution can change quickly for a newsvendor seller. We refer to sudden changes in demand distribution as demand shocks. When a newsvendor seller has limited demand distribution information and also experiences underlying demand shocks, the majority of existing methods for newsvendor problems may not work well since they either require demand distribution information or assume stationary demand distribution. We present a new, robust, and effective machine learning algorithm for newsvendor problems with demand shocks but without any demand distribution information. The algorithm needs only an approximate estimate of the lower and upper bounds of demand range; no other knowledge such as demand mean, variance, or distribution type is necessary. We establish the theoretical bounds that determine this machine learning algorithm's performance in handling demand shocks. Computational experiments show that this algorithm outperforms the traditional approaches in a variety of situations including large and frequent shocks of the demand mean. The method can also be used as a meta‐algorithm by incorporating other traditional approaches as experts. Working together, the original algorithm and the extended meta‐algorithm can help manufacturers and retailers better adapt their production and inventory control decisions in dynamic environments where demand information is limited and demand shocks are frequent      

Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.