Assortment Planning for Vertically Differentiated Products

We consider the problem of a retailer managing a category of vertically differentiated products. The retailer has to pay a fixed cost for each product included in the assortment and a variable cost per product sold. Quality levels, fixed, and variable costs are exogenously determined. Customers differ in their valuation of quality and choose the product (if any) that maximizes their utility. First, we consider a setting in which the selling prices are also fixed. We find that the optimal set of products to offer depends on the distribution of customer valuations and might include dominated products, that is, products which are less attractive than at least one other product, on every possible dimension. We develop an efficient algorithm to identify an optimal assortment. Second, we consider a setting in which the retailer also determines the selling prices. We show that in this case the optimal assortment does not include any dominated product and does not vary with the distribution of customer valuations when there is no fixed cost. We develop several efficient algorithms to identify an optimal assortment and optimally price the products. We also test the applicability of our methods with realistic data for two product categories.     

Bundling of Vertically Differentiated Products in a Supply Chain*

We consider a supply chain consisting of a single manufacturer and a single retailer. The manufacturer produces a basic and a premium product. If desired, a bundle of the two products might also be produced at a unit bundling cost. We allow either the manufacturer or the retailer to produce the bundle from the component products. All products, however, must be sold exclusively through the retailer. Using game theoretic models, we compare and contrast the equilibrium outcomes under retailer bundling and manufacturer bundling scenarios. We show that under manufacturer bundling, the manufacturer never offers the full product line composed of the basic product, the premium product, and the bundle, at equilibrium; while the same does not hold under retailer bundling. We show that total supply chain profit under retailer bundling weakly dominates that under manufacturer bundling and characterize the region in the parameter space where this domination is strict. We explore an extension where there is a capacity constraint in producing one or both of the component products and characterize the equilibrium outcomes. We show that unlike the infinite capacity case, offering the full product line is an equilibrium outcome under manufacturer bundling when the capacity of the premium good is limited.     

水平差异产品的内生定价策略选择

本文分析了一个存在定价策略选择下的三阶段Hotelling双头垄断模型,其中厂商可以选择采用单一定价策略或者歧视定价策略。模型的子博弈精炼纳什均衡表明厂商或者同时采用单一定价策略,或者同时采用歧视一价策略。当歧视定价的边际成本相对单一定价的边际成本不太高,或者消费乾注重产品特性差异时,厂商会同时选择歧视定价策略,尽管单一定价下厂商的利润要明显高于歧视定价下的利润;当歧视定价的边际成本相对较高或者消费者不太注重产品特性差异时,单一定价将成为厂商的最优选择。最后本文从社会最优的角度分析比较了两种这价策略下的社会净福利水平。     

The Impact of Limited Supply on a Firm's Bundling Strategy

A firm's two‐product bundling decision is examined when the supply of one product is limited and consumer valuations are normally distSteckeributed. The firm can choose to sell products separately and/or through a bundle. We find that the impact of limited supply on a firm's bundling decision depends on the correlation between the consumer valuations of the two products as well as the symmetry level of the two products in terms of their attractiveness (how much they are valued by consumers). When the valuation correlation is high and the symmetry level of the two products is low, limited supply can drive bundling. When the valuation correlation is low or the symmetry level is high, limited supply can drive no bundling. When the attractiveness of both products are low or the valuation correlation is very high, limited supply has no impact on a firm's bundling decision: The firm should not bundle for all supply levels. This study offers a new driver for product bundling: the limited supply of a product. The existing bundling literature suggests that a firm should bundle symmetric products that have a low consumer valuation correlation, when bundling is driven by consumer valuation heterogeneity reduction. In contrast, when bundling is driven by limited supply, a firm should bundle asymmetric products with a high consumer valuation correlation. The benefit of supply‐driven bundling depends on the severity of supply limitation. When supply limitation is moderate, bundling creates value by expanding the market of the less attractive product. When supply limitation is severe, bundling enables a firm to extract a higher margin from the less attractive product.     

Managing Supply Risk for Vertically Differentiated Co‐Products

The manufacturing complexity of many high‐tech products results in a substantial variation in the quality of the units produced. After manufacturing, the units are classified into vertically differentiated products. These products are typically obtained in uncontrollable fractions, leading to mismatches between their demand and supply. We focus on product stockouts due to the supply–demand mismatches. Existing literature suggests that when faced with product stockouts, firms should satisfy all unmet demand of a low‐end product by downgrading excess units of a high‐end product (downward substitution). However, this policy may be suboptimal if it is likely that low‐end customers will substitute with a higher quality product and pay the higher price (upward substitution). In this study, we investigate whether and how much downward substitution firms should perform. We also investigate whether and how much low‐end inventory firms should withhold to strategically divert some low‐end demand to the high‐end product. We first establish the existence of regions of co‐production technology and willingness of customers to substitute upward where firms adopt different substitution/withholding strategies. Then, we develop a managerial framework to determine the optimal selling strategy during the life cycle of technology products as profit margins shrink, manufacturing technology improves, and more capacity becomes available. Consistent trends exist for exogenous and endogenous prices.     

顾客策略行为下差异产品两阶段定价模型研究

互联网和信息技术的发展,为零售商收集顾客信息带来方便的同时,也使得消费者变得越来越具有策略性和选择性。首先,构建零售商只销售一种高质量产品的情形,研究其两阶段的定价策略,并分析产品的跨期折扣因子对产品的零售价格、销售量和零售商利润的影响。然后,考虑零售商可提供高质量和低质量两种产品的情形,顾客在第一销售期、第二销售期都可以选择两种产品。构建两阶段的定价决策模型,并分析产品的跨期折扣因子、顾客对低质量产品的接受度等参数对产品两阶段的零售价格、销售量的影响。最后,用数值算例分析了第二种模型下顾客对低质量产品的接受度等模型参数对零售商两阶段总利润的影响,然后比较了第一种和第二种模型下高质量产品的零售价格和销售量。研究结论较全面的分析了顾客策略行为对差异产品两阶段销售期的定价决策的影响,为零售商进行定价优化决策提供了十分重要的参考。     

电信服务与手机捆绑销售模式下考虑公平的均衡策略

本文以电信服务与手机捆绑销售模式为背景,研究了手机制造商主导下公平关切对手机制造商和服务运营商进行捆绑分销合作时的价格和补贴决策、利润分配以及补贴契约协调的影响。首先,分别给出了集中决策和补贴契约下捆绑销售渠道的最优均衡结果;然后,分析了补贴契约下手机制造商的公平关切对手机制造商和服务运营商的均衡策略、渠道各方利润以及整体利润的影响;进一步地,对捆绑销售模式下的补贴契约进行了协调性分析。研究结果表明：不利不公平厌恶将促使手机制造商制定一个较高的零售价格,从而恶化捆绑销售渠道的整体效益;有利不公平厌恶将促使手机制造商制定一个较低的零售价格,从而改善捆绑销售渠道的整体效益;然而,无论是否考虑手机制造商公平关切心理行为,补贴契约始终不能促使捆绑销售渠道实现协调;此外,手机制造商一味追求较高的利润分配比,并不一定能给自身带来更多利润,反而会降低整体利润。     

On Pricing and Composition of Bundles

This paper addresses the problem of how to determine the composition and price of a bundle so as to maximize the total expected profit. To motivate the problem, we use as a setting a high‐tech manufacturing company that operates in a competitive environment, is not a leader in the industry, and is constantly reacting to bundles introduced by the leader. Bundles are sets of components that must meet technical constraints. The company's objective is to build a bundle and offer it in a market where it will compete with other bundles. Consumers purchase the bundle that maximizes their utility after examining all available bundles. The company selection of the bundle's components and its price is made in light of the bundles against which it will be competing and the uncertainty in the consumer choice process. The optimal decision could be found by solving a nonlinear mixed integer program, which is difficult to solve. Instead, we propose an efficient solution procedure to determine the optimal composition of the bundle and the price at which it should be offered. The paper concludes with a brief discussion of extensions of the research to cases that consider multiple segments of customers and/or multiple bundles.     

Product Assortment and Price Competition under Multinomial Logit Demand

The role of assortment planning and pricing in shaping sales and profits of retailers is well documented and studied in monopolistic settings. However, such a role remains relatively unexplored in competitive environments. In this study, we study equilibrium behavior of competing retailers in two settings: (i) when prices are exogenously fixed, and retailers compete in assortments only; and (ii) when retailers compete jointly in assortment and prices. For this, we model consumer choice using a multinomial Logit, and assume that each retailer selects products from a predefined set, and faces a display constraint. We show that when the sets of products available to retailers do not overlap, there always exists one equilibrium that Pareto‐dominates all others, and that such an outcome can be reached through an iterative process of best responses. A direct corollary of our results is that competition leads a firm to offer a broader set of products compared to when it is operating as a monopolist, and to broader offerings in the market compared to a centralized planner. When some products are available to all retailers, that is, assortments might overlap, we show that display constraints drive equilibrium existence properties.     

Pricing and Replenishment of Competing Perishable Product Variants under Dynamic Demand Substitution

I consider pricing and ordering decisions faced by a retailer selling a perishable product with a two‐period shelf life over an infinite horizon. In the first period, the product is “new”; in the next, it becomes “old.” The new product is perceived by customers to have a higher quality than the old product. Every period, the retailer makes three decisions: prices for the new and old products and how much new product to order. I first show, with some simple cases, that demand uncertainty can make the sale of the old product profitable. I then consider a more realistic case with dynamic demand substitution among customers. I recognize that the retailer's decisions may be constant or may vary across different periods, under different contexts. For instance, varying the price of the new product can sometimes be difficult due to the negative impact it generates among customers. I find that (i) the benefit obtained from selling the old product with constant decisions is much higher than the benefit from allowing all the decisions to vary; (ii) the former benefit increases with a higher procurement cost, a higher quality of the new product, and higher demand volatility; however, the latter benefit is non‐monotone in these parameters; (iii) most of the latter benefit can be obtained by just changing the order quantity; and (iv) as the inventory of the old product increases, when all the decisions vary, the optimal price of the new product may increase or decrease.     

Identification in Differentiated Products Markets Using Market Level Data

We present new identification results for nonparametric models of differentiated products markets, using only market level observables. We specify a nonparametric random utility discrete choice model of demand allowing rich preference heterogeneity, product/market unobservables, and endogenous prices. Our supply model posits nonparametric cost functions, allows latent cost shocks, and nests a range of standard oligopoly models. We consider identification of demand, identification of changes in aggregate consumer welfare, identification of marginal costs, identification of firms' marginal cost functions, and discrimination between alternative models of firm conduct. We explore two complementary approaches. The first demonstrates identification under the same nonparametric instrumental variables conditions required for identification of regression models. The second treats demand and supply in a system of nonparametric simultaneous equations, leading to constructive proofs exploiting exogenous variation in demand shifters and cost shifters. We also derive testable restrictions that provide the first general formalization of Bresnahan's (1982) intuition for empirically distinguishing between alternative models of oligopoly competition. From a practical perspective, our results clarify the types of instrumental variables needed with market level data, including tradeoffs between functional form and exclusion restrictions.     

Pareto‐Improving Contracts for Express Package Delivery Services

We address the problem of an express package delivery company in structuring a long‐term customer contract whose terms may include prices that differ by day‐of‐week and by speed‐of‐service. The company traditionally offered speed‐of‐service pricing to its customers, but without day‐of‐week differentiation, resulting in customer demands with considerable day‐of‐week seasonality. The package delivery company hoped that using day‐of‐week and speed‐of‐service price differentiation for contract customers would induce these customers to adjust their demands to become counter‐cyclical to the non‐contract demand. Although this usually cannot be achieved by pricing alone, we devise an approach that utilizes day‐of‐week and speed‐of‐service pricing as an element of a Pareto‐improving contract. The contract provides the lowest‐cost arrangement for the package delivery company while ensuring that the customer is at least as well off as he would have been under the existing pricing structure. The contract pricing smoothes the package delivery company's demand and reduces peak requirements for transport capacity. The latter helps to decrease capital costs, which may allow a further price reduction for the customer. We formulate the pricing problem as a biconvex optimization model, and present a methodology for designing the contract and numerical examples that illustrate the achievable savings.     

基于战略顾客行为的质量差异化产品定价策略

采用博弈论方法构建竞争企业两周期动态定价模型,研究基于战略顾客行为的质量差异化产品最优定价策略,并分析基于行为的定价(behavior-based pricing,BBP) 对企业利润的影响. 研究结论表明：1)企业相对生产效率和决策顺序是影响BBP策略选择的关键因素;2)当竞争企业相对生产效率差异较大时,BBP策略保护弱势企业利润并且损害强势企业利润,从而加剧行业竞争;3)拥有信息优势的企业单独采用BBP策略时,不仅自身利润降低,也会损害竞争对手利润,从而导致“损人不利己”的双输局面,这与直觉相悖. 最后,选择实际企业数据对本文的模型和结论进行说明验证.     

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

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

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.     

专利技术授权、产品分销与分销渠道选择研究

从专利技术转化为现实生产力的视角,为研究技术供应商、制造商以及零售商之间的专利技术授权与分销渠道选择问题,构建不同渠道结构下的经济模型。通过模型求解,得到最优专利技术授权与产品定价决策以及分销渠道策略。研究发现：1)在专利技术授权阶段,技术供应商会策略性地选择仅包含固定授权费或者“版税提成+固定授权费”形式的授权合同;2)在产品分销阶段,制造商根据渠道成本、消费者渠道偏好、市场规模等因素来选择不同渠道结构,包括单渠道分销策略和双渠道分销策略;3)不同分销渠道选择不会影响授权合同形式,但会促使技术供应商和制造商调整各自的最优决策。最后,对原始模型进行不同维度的扩展,探究第三方电商平台模式、零售商渠道入侵模式等情形下的专利技术授权问题。     

基于异质性消费群体的再制造产品的定价策略研究

消费者对新产品和再制造产品具有不同支付意愿。在此基础上,对再制造产品具有不同接受度的异质性消费群体分别建立了再制造产品差异化定价模型和单一定价策略模型。研究了制造商对新产品和再制造产品进行差异化定价时,新产品和再制造产品的最优定价和与之相对应的产品回收率,并与单一定价策略进行了比较分析。通过数值仿真,讨论了不同参数对单一定价策略和差异化定价策略的利润和产品回收率的影响,并给出了相关结论。     

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

基于降价预期的生鲜农产品定价策略研究

顾客的价格感知影响需求。以降价预期刻画顾客对当前价格的感知,针对零售商在维持需求和利润最大化条件下降价两种策略,研究了生鲜农产品的最优定价问题。研究表明,零售商的利润随着价格认同系数增加而增大;顾客对独立产品存在降价预期不会影响零售商的利润,但是对替代品存在降价预期,零售商的利润会下降;零售商若能完全观察到顾客存在降价预期,将抬高初始价格。