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.     

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.     

Service Systems with Experience‐Based Anecdotal Reasoning Customers

The existing queueing literature typically assumes that customers either perfectly know the expected waiting time or are able to form rational expectations about it. In contrast, in this article, we study canonical service models where customers do not have such full information or capability. We assume that customers lack full capability or ample opportunities to perfectly infer the service rate or estimate the expected waiting time, and thus can only rely on past experiences and anecdotal reasoning to make their joining decisions. We fully characterize the steady‐state equilibrium in this service system. Compared with the fully rational benchmark, we find that customers with anecdotal reasoning are less price‐sensitive. Consequently, with a higher market potential (higher arrival rate), a revenue‐maximizing firm may increase the price if the service rate is exogenous, and it may decrease the price if the service rate is at the firm's discretion. Both results go against the commonly accepted pricing recommendations in the fully rational benchmark. We also show that revenue maximization and welfare maximization lead to fundamentally different pricing strategies with anecdotal reasoning, whereas they are equivalent in the fully rational benchmark.     

考虑战略顾客行为时的供应链性能分析与协调

动态定价策略的广泛应用使得越来越多的顾客具有了战略性,战略顾客会根据产品在销售期内的价格路径确定最优购买时机,零售商则根据顾客的购买行为确定订货数量和销售价格.研究了双方静态博弈时的理性预期均衡解和零售商进行数量承诺时的情形.研究表明:理性预期均衡时的最优销售价格、最优存货数量和最优期望利润分别小于标准报童模型的情形;数量承诺时的最优存货数量小于理性预期均衡时的最优存货数量;最优期望利润则大于理性预期均衡时的最优期望利润,并且在一定条件下可能会大于标准报童模型的最优期望利润,战略顾客行为的存在对零售商可能有利.最后分析了在分散式供应链中如何利用收入分享契约和数量折扣契约实现供应链协调.     

Optimal Uniform Pricing Strategy of a Service Firm When Facing Two Classes of Customers

When facing heterogeneous customers, how should a service firm make its pricing decision to maximize revenue? If discrimination is allowed, then priority schemes and differentiated pricing are often used to achieve that. In many applications, however, the firm cannot or is not allowed to set discriminatory prices, for example, list price in retail stores, online shopping, and gas stations; thus a uniform price must be applied to all customers. This study addresses the optimal uniform pricing problem of a service firm using a queueing system with two classes of customers. Our result shows that the potential pool of customers plays a central role in the firm's optimal decision. Depending on the range of system parameters, which are determined explicitly by the primitive data, the firm's optimal strategy may choose to serve only one class of customers, a subset of a class of customers, or a combination of different classes of customers. In addition, the optimal price is in general not monotonic with respect to the potential market sizes because their changes may lead to a major shift in the firm's decision on which customer class to serve. However, unless such a shift occurs, the optimal price is weakly decreasing in the potential market sizes.     

Static and Dynamic Pricing of Excess Capacity in a Make‐to‐Order Environment

We consider a make‐to‐order manufacturer that serves two customer classes: core customers who pay a fixed negotiated price, and “fill‐in” customers who make submittal decisions based on the current price set by the firm. Using a Markovian queueing model, we determine how much the firm can gain by explicitly accounting for the status of its production facility in making pricing decisions. Specifically, we examine three pricing policies: (1) static, state‐independent pricing, (2) constant pricing up to a cutoff state, and (3) general state‐dependent pricing. We determine properties of each policy, and illustrate numerically the financial gains that the firm can achieve by following each policy as compared with simpler policies. Our main result is that constant pricing up to a cutoff state can dramatically outperform a state‐independent policy, while at the same time achieving most of the increase in revenue achievable from general state‐dependent pricing. Thus, we find that constant pricing up to a cutoff state presents an attractive tradeoff between ease of implementation and revenue gain. When the costs of policy design and implementation are taken into account, this simple heuristic may actually out‐perform general state‐dependent pricing in some settings.     

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.     

Flexible Capacity Investments and Product Mix: Optimal Decisions and Value of Postponement Options

In this article, we study a firm's interdependent decisions in investing in flexible capacity, capacity allocation to individual products, and eventual production quantities and pricing in meeting uncertain demand. We propose a three‐stage sequential decision model to analyze the firm's decisions, with the firm being a value maximizer owned by risk‐averse investors. At the beginning of the time horizon, the firm sets the flexible capacity level using an aggregate demand forecast on the envelope of products its flexible resources can accommodate. The aggregate demand forecast evolves as a Geometric Brownian Motion process. The potential market share of each product is determined by the Multinomial Logit model. At a later time and before the end of the time horizon, the firm makes a capacity commitment decision on the allocation of the flexible capacity to each product. Finally, at the end of the time horizon, the firm observes the demand and makes the production quantity and pricing decisions for end products. We obtain the optimal solutions at each decision stage and investigate their optimal properties. Our numerical study investigates the value of the postponed capacity commitment option in supplying uncertain operation environments.     

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.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

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.     

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。     

Dynamic Customer Acquisition and Retention Management

In consulting, finance, and other service industries, customers represent a revenue stream, and must be acquired and retained over time. In this paper, we study the resource allocation problem of a profit maximizing service firm that dynamically allocates its resources toward acquiring new clients and retaining unsatisfied existing ones. The interaction between acquisition and retention in our model is reflected in the cash constraint on total expected spending on acquisition and retention in each period. We formulate this problem as a dynamic program in which the firm makes decisions in both acquisition and retention after observing the current size of its customer base and receiving information about customers in danger of attrition, and we characterize the structure of the optimal acquisition and retention strategy. We show that when the firm's customer base size is relatively low, the firm should spend heavily on acquisition and try to retain every unhappy customer. However, as its customer base grows, the firm should gradually shift its emphasis from acquisition to retention, and it should also aim to strike a balance between acquisition and retention while spending its available resources. Finally, when the customer base is large enough, it may be optimal for the firm to begin spending less in both acquisition and retention. We also extend our analysis to situations where acquisition or retention success rate, as a function of resources allocation, is uncertain and show that the optimal acquisition and retention policy can be surprisingly complex. However, we develop an effective heuristic for that case. This paper aims to provide service managers some analytical principles and effective guidelines on resource allocation between these two significant activities based on their firm's customer base size.     

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.     

Selling Finite Capacity in Bulks*

We consider a firm that owns a limited capacity for the delivery of services or for the production of customized products. Potential buyers specify the amount of capacity they will require for the execution of their intended services, goods or projects. Based on the size of the requirement, the firm makes a bid while being challenged in various ways: (1) it only knows the underlying probability function from which its customers’ reservation prices are drawn, (2) arrival of additional future requests is stochastic, and, (3) the firm knows in advance neither the magnitude of these potential requests nor the buyer's reservation price. The firm aims to maximize its expected profit by choosing its pricing mechanism. The fact that capacity is demanded in varying amounts distinguishes this problem from most available literature in which standard sizes are sold or partial fulfillment and displacement are permitted. Lacking such allowances presents a new challenge to the firm as in conjunction with pricing it should also address the issue of various sizes requests’ compatibility to achieve optimal utilization of its capacity in order to maximize expected profit. In this article, we consider two approaches of handling this problem: myopic and foresighted. We formulate and analyze the problem to obtain the firm's optimal bidding decisions as well as managerial insight about the optimal bid level and its important role in coordinating buyers’ requests. Furthermore, due to this role, pricing patterns in this environment are different than those in standard unit sales.     

Coordinating Sales and Raw Material Discounts in a Global Supply Chain

In this paper, the supplier of a key component to a global manufacturer offers a one‐time price discount; we study the firm's optimal response to the discount under two different strategies. In the first strategy, the firm does not pass along the discount to its customers (sales subsidiaries); the firm simply coordinates purchasing and production among the different factories to take advantage of this one‐time price discount. In the second strategy, the firm offers price discounts for its most profitable products in different sales subsidiaries to increase their demand. We carried out experiments for the two strategies based on a mathematical programming model, built around Toshiba's global notebook supply chain. Model constraints include, among others, material constraints, bill‐of‐materials, capacity and transportation constraints, minimum lot size constraints, and a constraint on minimum fill rate (service level constraint). Unlike most models of this type in the literature, which define variables in terms of single arc flows, we employ path variables, which allow for direct identification and manipulation of profitable and non‐profitable products.     

Customer Behavior in an Online Ordering Application: A Decision Scoring Model*

This research presents the development of behavioral scoring models to predict future customer purchases in an online ordering application. Internet retailing lowers many barriers for customers switching between retailers for repeat purchases; thus, retaining existing customers is a key challenge for achieving profitability. Survey data were collected from 1,089 online customers of two companies. The subjective survey data were then used to predict purchases over the ensuing 12 months based on data from the company databases. The analysis illustrates the general applicability of predictive models of future customer purchases while also demonstrating the need to develop specific models tailored for an individual company's operating and marketing environment. The models provide insight on how companies can target marketing dollars more effectively and allocate investment across multiple operational areas for maximum return. The research answers a call for rigorous research in the area of predictive marketing, an area in which many companies are excelling but where there is a scarcity of detailed knowledge regarding application of such models.     

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。     

Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

Pricing Strategies under Behavioral Observational Learning in Social Networks

The increasing pervasiveness of social networks allows users to share purchase behaviors with their online friends. In this study, we examine optimal pricing strategies of a monopolistic firm using an analytical model that accounts for behavioral observational learning in social networks. We show that a seller could potentially control the information available to future customers and induce behavioral observational learning, using an information‐revealing pricing strategy. This result suggests that offering introductory discounts is not always an effective method to boost purchases in social networks. It could prevent the behavioral observational learning that would increase future customers' willingness to pay.