Optimal Pricing of Two Successive‐Generation Products with Trade‐in Options under Uncertainty

To entice consumers to purchase both current and next generation products, many manufacturers and retailers offer trade‐in programs that allow buyers of the first generation product to trade‐in the product and purchase the new generation product at a lower price. By considering the interactions between “forward‐looking” consumers and a firm when a trade‐in program is offered, we analyze a two‐period dynamic game to determine the optimal prices of two successive‐generation products in equilibrium, and examine the conditions under which trade‐in programs are beneficial to the firm. Our model incorporates market heterogeneity (valuation of the first generation product varies among the consumer population), product uncertainty (the incremental value of the new product is uncertain before its introduction), and consumers' forward‐looking behavior (consumers take future product valuation and prices into consideration when making purchasing decisions). With the trade‐in option, we show that consumers are willing to pay a price that is higher than their valuations of the current product. Furthermore, trade‐in programs are more beneficial to the firm when: (i) the durability of the current product is high; (ii) the market heterogeneity is low; or (iii) the uncertainty level (or the expected incremental value) of the new product is high. Finally, when the incremental value of the new product is more uncertain, consumers are more willing to purchase the current product because of the “option” value of the trade‐in programs and thus trade‐in programs can be more beneficial to the firm in this case.     

焕新计划下考虑消费者细分的产品定价策略

焕新计划是生产商为提升自身竞争优势而推出的一种促销手段，加入焕新计划的消费者在第一阶段可以享受全方位服务，在第二阶段可以享受以旧换新抵扣优惠。消费者将权衡加入焕新计划的费用、服务水平以及抵扣力度等因素决策是否在第一阶段加入焕新计划。本文假设时尚型消费者每阶段都会购买最新产品，而节俭型消费者第一阶段购买产品后在第二阶段继续使用，针对这两类消费者在实施焕新计划和不实施焕新计划两种情况下，构建两阶段模型以决策产品的最优定价；运用解析方法分析了产品的生产成本等参数对最优定价的影响；运用解析方法和数值算例方法对两模型进行对比。     

Customer‐Base Concentration and Inventory Efficiencies: Evidence from the Manufacturing Sector

What is the link between customer‐base concentration and inventory efficiencies in the manufacturing sector? Using hand‐collected data from 10‐K Filings, we find that manufacturers with more concentrated customer bases hold fewer inventories for less time and are less likely to end up with excess inventories, as indicated by the lower likelihood and magnitude of inventory write‐downs and reversals. Using disaggregated inventory disclosures, we find that inventory efficiencies primarily flow through the finished goods inventory account, while raw material efficiencies are offset by higher work‐in‐process holdings and longer work‐in‐process cycles. In additional analysis, we document a valuation premium for more concentrated manufacturers after controlling for other firm characteristics, including default risk and cost of capital estimates. We conclude that investors trade off the costs and benefits of relationships with a limited number of major customers and, on balance, consider customer‐base concentration as a net positive for firm valuation. Overall, our study adds to interdisciplinary research in accounting and operations management by shedding new light on the relevance of major customer disclosures for fundamental analysis and valuation in the manufacturing sector.     

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.     

Revenue Management with End‐of‐Period Discounts in the Presence of Customer Learning

Consider a firm that sells identical products over a series of selling periods (e.g., weekly all‐inclusive vacations at the same resort). To stimulate demand and enhance revenue, in some periods, the firm may choose to offer a part of its available inventory at a discount. As customers learn to expect such discounts, a fraction may wait rather than purchase at a regular price. A problem the firm faces is how to incorporate this waiting and learning into its revenue management decisions. To address this problem we summarize two types of learning behaviors and propose a general model that allows for both stochastic consumer demand and stochastic waiting. For the case with two customer classes, we develop a novel solution approach to the resulting dynamic program. We then examine two simplified models, where either the demand or the waiting behavior are deterministic, and present the solution in a closed form. We extend the model to incorporate three customer classes and discuss the effects of overselling the capacity and bumping customers. Through numerical simulations we study the value of offering end‐of‐period deals optimally and analyze how this value changes under different consumer behavior and demand scenarios.     

Will More Purchasing Options Benefit Customers?

This paper considers the sale of a seasonal product in the face of strategic customers. At the beginning of the selling season, the retailer announces both the price p_h at which the product will be sold during the selling season and the post‐season clearance price p<p_h for unsold items. We analyze two operating regimes: The “no reservation regime” allows a buyer either to purchase the product at price p_h when he arrives or to enter a lottery to purchase at price p if the product remains unsold. The “reservation regime” offers each buyer one extra option than the no reservation regime: reserve the product for purchase at the clearance price p. If the buyer reserves the product under the reservation regime and if it remains unsold at the end of the selling season, then he is obligated to purchase it at price p. We consider a situation in which heterogeneous customers with probabilistic valuation arrive in accord with a Poisson process. We characterize the rational purchasing behavior wherein each arriving customer is strategic; each customer takes other customers' purchasing behavior into consideration. By considering the Nash equilibrium of this game, we show that strategic customer behavior can render the customer to be worse off and the retailer to be better off under the reservation regime, despite the fact that this regime offers one extra option (reservation) to a customer. Hence, more purchasing options do not necessarily benefit customers.     

Equilibrium Joining Strategies and Optimal Control of a Make‐to‐Stock Queue

We consider a make‐to‐stock, finite‐capacity production system with setup cost and delay‐sensitive customers. To balance the setup and inventory related costs, the production manager adopts a two‐critical‐number control policy, where the production starts when the number of waiting customers reaches a certain level and shuts down when a certain quantity of inventory has accumulated. Once the production is set up, the unit production time follows an exponential distribution. Potential customers arrive according to a Poisson process. Customers are strategic, i.e., they make decisions on whether to stay for the product or to leave without purchase based on their utility values, which depend on the production manager's control decisions. We formulate the problem as a Stackelberg game between the production manager and the customers, where the former is the game leader. We first derive the equilibrium customer purchasing strategy and system performance. We then formulate the expected cost rate function for the production system and present a search algorithm for obtaining the optimal values of the two control variables. We further analyze the characteristics of the optimal solution numerically and compare them with the situation where the customers are non‐strategic.     

A Choice‐Based Dynamic Programming Approach for Setting Opaque Prices

Opaque pricing is a form of pricing where certain characteristics of the product or service are hidden from the consumer until after purchase. In essence, opaque selling transforms a differentiated good into a commodity. Opaque pricing has become popular in service pricing as it allows firms to sell their differentiated product at higher prices to regular brand loyal customers while simultaneously selling to non‐brand loyal customers at discounted prices. We use a nested logit model in combination with logistic regression and dynamic programming to illustrate how a service firm can optimally set prices on an opaque sales channel. The choice model allows the characterization of consumer trade‐offs when purchasing opaque products while the dynamic programming approach allows the characterization of the optimal pricing policy as a function of inventory and time remaining. We compare optimal prices and expected revenues when dynamic pricing is restricted to daily price changes. We provide an illustrative example using data from an opaque selling mechanism ( Hotwire.com ) and a Washington DC‐based hotel.     

Browse‐and‐Switch: Retail‐Online Competition under Value Uncertainty

Although online shopping is becoming popular, consumers who are unsure about whether to buy a product may find it advantageous to visit a brick‐and‐mortar retail store to first examine the product before purchasing it. But, after browsing at the store, consumers have the option of switching to an e‐tailer to purchase the item at a cheaper price rather than buying at the store. Recent business press refers to this browse‐and‐switch behavior as “showrooming,” and attributes to it the declining profits of brick‐and‐mortar retailers. To study the effect of the browse‐and‐switch option on retail and online pricing strategies and profits, we analyze a stylized economic model that incorporates uncertainty in consumers' valuation of the product, captures the heterogeneity among consumers in their inclination to purchase online, and permits product returns. We consider various equilibrium scenarios for different combinations of consumer shopping behaviors, characterize the parameter ranges for each scenario, and demonstrate that browse‐and‐switch behavior can indeed occur under equilibrium. Our analysis further shows that the option for consumers to browse‐and‐switch intensifies competition, reducing the profits for both firms.     

Self‐Service Operations at Retail Stores: The Role of Inter‐Customer Interactions

Inter‐customer interactions are important to the operation of self‐services in retail settings. More specifically, when self‐service terminals are used as part of customers’ checkout processes in retail operations without the explicit involvement of retailers as the direct service providers, inter‐customer interactions become a significant managerial issue. In this article, we examine the impact of inter‐customer interactions at retail self‐service terminals on customers’ service quality perceptions and repeat purchase intentions at retail stores. We conduct a scenario‐based experimental design (N = 674) using a 2 × 2 factorial design in which inter‐customer interactions are divided into “positive” vs. “negative” and occur during the “waiting” or during the actual “transaction” stages of self‐services at a retail store. We use attribution theory to develop the hypotheses. The results demonstrate that, through their interactions, fellow customers can exert influences on a focal customer's quality perceptions and repeat purchasing intentions toward a retail store. Furthermore, these influences were impacted by how customers attribute blame or assign responsibility toward the retail store. Service operations managers should leverage these interactions by designing into self‐service settings the capacities and interfaces that are best suited for customers’ co‐production of their self‐service experiences.     

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.     

CEO Incentives and Customer‐Supplier Relations

This study explores how suppliers adjust their relation‐specific investments (RSI) in response to the different risk‐taking incentives provided by the customer firm to its CEO, during normal and transition periods. We investigate this relation using 17,553 customer–supplier transactions over the 1993–2013 period. We find strong evidence consistent with the risk‐taking argument. Specifically, we find that an increase in the risk‐taking incentives of customer CEOs leads to a decline in suppliers’ RSI in normal periods, but an increase in RSI during transition periods. We employ the FAS‐123R mandate to show that an exogenous reduction in customer CEO's incentive pay increases suppliers’ RSI. We reaffirm the effect with the passage of the Sarbanes–Oxley Act as a secondary quasi‐natural experiment. Finally, we examine several scenarios that either amplify or attenuate the observed relation, based on factors such as financial constraints, distress, growth opportunities, industry competition, and other firm characteristics. Our study contributes to the literature that examines the interplay between corporate policy and product market relationships.     

End‐of‐Life Inventory Problem with Phaseout Returns

We consider the service parts end‐of‐life inventory problem of a capital goods manufacturer in the final phase of its life cycle. The final phase starts as soon as the production of parts terminates and continues until the last service contract expires. Final order quantities are considered a popular tactic to sustain service fulfillment obligations and to mitigate the effect of obsolescence. In addition to the final order quantity, other sources to obtain serviceable parts are repairing returned defective items and retrieving parts from phaseout returns. Phaseout returns happen when a customer replaces an old system platform with a next‐generation one and returns the old product to the original equipment manufacturer (OEM). These returns can well serve the demand for service parts of other customers still using the old generation of the product. In this study, we study the decision‐making complications as well as cost‐saving opportunities stemming from phaseout occurrence. We use a finite‐horizon Markov decision process to characterize the structure of the optimal inventory control policy. We show that the optimal policy consists of a time‐varying threshold level for item repair. Furthermore, we study the value of phaseout information by extending the results to cases with an uncertain phaseout quantity or an uncertain schedule. Numerical analysis sheds light on the advantages of the optimal policy compared to some heuristic policies.     

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.     

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.     

Sequence Matters: Shelf‐Space Allocation under Dynamic Customer‐Driven Substitution

Customers who face a stockout situation often decide to purchase a different product in the same category. We analyze the resulting dynamic substitution problem in a retail environment, where customers serve themselves from the store shelves, such that the sequence of customer arrivals affects how scarce products are allocated to customers. We consider a setting with constrained shelf space, and we study how a retailer should optimally allocate such space between substitute products. We characterize environments where the sequence of customer arrivals can have a substantial impact on profitability.     

Improving Valuation Under Consumer Search: Implications for Pricing and Profits

There is a growing trend in the retail industry to improve customer experience. In this article, we study retailer‐initiated strategies to increase consumer valuation for a product under duopoly. In such a setting, it is possible that a consumer's valuation may be increased by one retailer; however, the consumer may decide to buy the product from the competitor. We consider a two‐stage game where retailers first decide whether to invest in improvements in customer valuation and then engage in price competition. We computationally explore the Nash equilibria in terms of both investment and pricing. We find that in the majority of cases retailers price in a manner to discourage their local customers to buy from the competitor. Next, we focus on the pricing game and theoretically characterize the pricing Nash equilibrium. We find that a retailer could overcome competitive effects by improving consumer valuation beyond a certain threshold. We also find that a retailer who does not invest could benefit from competition in situations where his competitor increases consumer valuation beyond a threshold. Finally, we explore through a computational study the Nash equilibria of the two‐stage game using an alternate model to establish the robustness of our findings.     

TIME‐BASED PRICING AND LEADTIME POLICIES FOR A BUILD‐TO‐ORDER MANUFACTURER

We studied time‐based policies on pricing and leadtime for a build‐to‐order and direct sales manufacturer. It is assumed that the utility of the product varies among potential customers and decreases over time, and that a potential customer will place an order if his or her utility is higher than the manufacturer's posted price. Once an order is placed, it will be delivered to the customer after a length of time called “leadtime.” Because of the decrease in a customer's utility during leadtime, a customer will cancel the order if the utility falls below the ordering price before the order is received. The manufacturer may choose to offer discounted prices to customers who would otherwise cancel their orders. We discuss two price policies: common discounted price and customized discounted price. In the common discounted price policy, the manufacturer offers a single lower price to the customers; in the customized discounted price policy, the manufacturer offers the customers separately for individual new prices. Our analytical and numerical studies show that the discounted price policies results in higher revenue and that the customized discounted price policy significantly outperforms the common discounted price policy when product utility decreases rapidly. We also study two leadtime policies when production cost decreases over time. The first uses a fixed leadtime, and the second allows the leadtime to vary dynamically over time. We find that the dynamic leadtime policy significantly outperforms the fixed leadtime policy when the product cost decreases rapidly.     

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.     

Toward a Differentiated Understanding of the Value‐Creation Chain

The conventional view of the value‐creation chain suggests offering high‐value propositions at the product level (in terms of benefits provided by elements of the product) to attain high‐value perceptions at the customer level, which should ultimately result in high‐value appropriation at the firm level (i.e. relationship, volume, pricing and financial success). This study challenges this view and provides a differentiated understanding of the value‐creation chain. With a multi‐industry sample of 339 companies and a sample of 626 customers to validate managerial assessments, the authors apply a configurational approach to identify whether and to what extent offering high‐value propositions at the product level is necessary or sufficient for achieving superior value perceptions at the customer level and high‐value appropriation at the firm level. Taking into account the company‐internal and company‐external environment of the value‐creation chain, the study identifies seven value‐creation chain constellations.