Joint Ordering and Pricing Strategies for Managing Substitutable Products

Starr and Rubinson (1978) develop a model to establish the relationship between product demand and relative prices. The notion of relative prices motivates us to consider a situation in which a retailer would either charge the same retail price for all products if he adopts a ‘fixed’ pricing strategy or charge different prices for different products if he adopts a ‘variable’ pricing strategy. In this paper, we develop a base model with deterministic demand that is intended to examine how a retailer should jointly determine the order quantity and the retail price of two substitutable products under the fixed and variable pricing strategies. Our analysis indicates that the optimal retail price under the variable pricing strategy is equal to the optimal retail price under the fixed pricing strategy plus or minus an adjustment term. This adjustment term depends on product substitutability and price sensitivity. We also present two different extensions of our base model. In the first extension, our analysis indicates that the underlying structure of the optimal retail price and order quantity is preserved when there is a limit on the total order quantity. The second extension deals with the issue of retail competition. Relative to the base case, we show that the underlying structure of the optimal retail price and order quantity is preserved in a duopolistic environment. Moreover, our analysis suggests that both retailers would adopt the variable pricing strategy at the equilibrium.     

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

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.     

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。     

A Competitive Model of Customization with Lead‐Time Effects

In this article, we study the competitive interactions between a firm producing standard products and a firm producing custom products. Consumers with heterogeneous preferences choose between n standard products, which may not meet their preferences exactly but are available immediately, and a custom product, available only after a certain lead time l. Standard products incur a variety cost that increases with n and custom products incur a lead time cost that is decreasing in the lead time l. We consider a two‐stage game wherein at stage 1, the standard product firm chooses the variety and the custom firm chooses the lead time and then both firms set prices simultaneously. We characterize the subgame‐perfect Nash equilibrium of the game. We find that both firms can coexist in equilibrium, either sharing the market as local monopolists or in a price‐competitive mode. The standard product firm may offer significant or minimal variety depending on the equilibrium outcome. We provide several interesting insights on the variety, lead time, and prices of the products offered and on the impact of problem parameters on the equilibrium outcomes. For instance, we show that the profit margin and price of the custom product are likely to be higher than that of standard products in equilibrium under certain conditions. Also, custom firms are more likely to survive and succeed in product markets with larger potential market sizes. Another interesting insight is that increased consumer sensitivity to product fit may result in lower lead time for the custom product.     

Impact of Price Postponement on Capacity and Flexibility Investment Decisions

Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made.     

Centralized versus Decentralized Competition for Price and Lead‐Time Sensitive Demand

We study two firms that compete on price and lead‐time decisions in a common market. We explore the impact of decentralizing these decisions, as made by the marketing and production departments, respectively, with either marketing or production as the leader. We compare scenarios in which none, one, or both of the firms are decentralized to see whether decentralization can be the equilibrium strategy. We find that under intense price competition, with intensity characterized by the underlying parameters of market demand, firms may suffer from a decentralized structure, particularly under high flexibility induced by high capacity, where revenue‐based sales incentives motivate sales/marketing to make aggressive price cuts that often erode profit margins. In contrast, under intense lead‐time competition, a decentralized strategy with marketing as the leader can not only result in significantly higher profits, but also be the equilibrium strategy. Moreover, decentralization may no longer lead to lower prices or longer lead‐times if the production department chooses capacity along with lead‐time.      

Technical Note – Pricing Below Cost Under Exchange‐Rate Risk

Pricing below cost is often classified as “dumping” in international trade and as “predatory pricing” in local markets. It is legally prohibited from practice because of earlier findings that it leads to predatory behavior by either eliminating competition or stealing market share. This study shows that a stochastic exchange rate can create incentives for a profit‐minded monopoly firm to set price below marginal cost. Our result departs from earlier findings because the optimal pricing decision is based on a rational behavior that does not exhibit any malicious intent against the competition to be considered as violating anti‐trust laws. The finding is a robust result, because our analysis demonstrates that this behavior occurs under various settings such as when the firm (i) is risk‐averse, (ii) can postpone prices until after exchange rates are realized, (iii) is capable of manufacturing in multiple countries, and (iv) operates under demand uncertainty in addition to the random exchange rate.     

竞争中的参考价格效应及承诺

消费者的社会感知会影响其对产品和品牌的评价。当消费者进行购买选择时,经常会受到参考价格效应的影响。而广告和价格不仅是企业经常要考虑的重要决策,还会对参考价格产生重要影响。为此,一个值得研究的的问题是：在考虑参考价格效应的情况下,企业该怎样确定其动态广告和价格策略？
为了研究该问题,本文构建了一个广告和价格的动态模型,来研究一个双寡头市场环境下两个寡头企业的价格和广告决策,并以此分析参考价格效应的作用。具体而言,我们假定企业可以采用广告承诺和价格承诺中的一种,其中前者承诺其在一段时间内的广告投入量恒定不变,而后者确保价格不变。两种策略不仅会影响消费者的购买决策,也会影响竞争对手的选择。在上述假定下,我们探讨了两个寡头企业在都采用广告承诺、都采用价格承诺及一个企业采用广告承诺而另一个企业采用价格承诺等三种不同情形下的最优广告和价格决策,并以此分析了三种情形下参考价格效应对最优的广告投入及定价策略的影响。最后,通过数值分析,探讨了不同情形下企业的最优策略选择。     

The Effect of Competition on the Efficient–Responsive Choice

In determining their operations strategy, a firm chooses whether to be responsive or efficient. For firms competing in a market with uncertain demand and varying intensity of substitutability for the competitor's product, we characterize the responsive or efficient choice in equilibrium. To focus first on the competitive implications, we study a model where a firm can choose to be responsive at no additional fixed or marginal cost. We find that competing firms will choose the same configuration (responsive or efficient), and responsiveness tends to be favorable when demand uncertainty is high or when product competition is not too strong. Intense competition can drive firms to choose to be efficient rather than responsive even when there is no additional cost of being responsive. In such a case, both firms would be better off by choosing to be responsive but cannot credibly commit. We extend the basic model to study the impact of endogenized production timing, multiple productions and product holdback (or, equivalently, postponed production). For all these settings, we find structurally similar results; firms choose the same configuration, and the firms may miss Pareto‐improvements. Furthermore, through extensions to the basic model, we find that greater operational flexibility can make responsiveness look less attractive in the presence of product competition. In contrast to our basic model and other extensions, we find it is possible for one firm to be responsive while the other is efficient when there is either a fixed cost or variable cost premium associated with responsive delivery.     

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.     

Measuring Market Power in the Ready‐to‐Eat Cereal Industry

The ready‐to‐eat cereal industry is characterized by high concentration, high price‐cost margins, large advertising‐to‐sales ratios, and numerous introductions of new products. Previous researchers have concluded that the ready‐to‐eat cereal industry is a classic example of an industry with nearly collusive pricing behavior and intense nonprice competition. This paper empirically examines this conclusion. In particular, I estimate price‐cost margins, but more importantly I am able empirically to separate these margins into three sources: (i) that which is due to product differentiation; (ii) that which is due to multi‐product firm pricing; and (iii) that due to potential price collusion. The results suggest that given the demand for different brands of cereal, the first two effects explain most of the observed price‐cost margins. I conclude that prices in the industry are consistent with noncollusive pricing behavior, despite the high price‐cost margins. Leading firms are able to maintain a portfolio of differentiated products and influence the perceived product quality. It is these two factors that lead to high price‐cost margins.     

Coping with Gray Markets: The Impact of Market Conditions and Product Characteristics

Gray markets, also known as parallel imports, have created fierce competition for manufacturers in many industries. We analyze the impact of parallel importation on a price‐setting manufacturer that serves two markets with uncertain demand, and characterize her policy against parallel importation. We show that ignoring demand uncertainty can take a significant toll on the manufacturer's profit, highlighting the value of making price and quantity decisions jointly. We find that adjusting prices is more effective in controlling gray market activity than reducing product availability, and that parallel importation forces the manufacturer to reduce her price gap while demand uncertainty forces her to lower prices. Furthermore, we explore the impact of market conditions (such as market base, price sensitivity, and demand uncertainty) and product characteristics (“fashion” vs. “commodity”) on the manufacturer's policy towards parallel importation. We also provide managerial insights about the value of strategic decision‐making by comparing the optimal policy to the uniform pricing policy that has been adopted by some companies to eliminate gray markets entirely. The comparison indicates that the value of making price and quantity decisions strategically is highest for moderately different market conditions and non‐commodity products.     

Dynamic Pricing to Minimize Maximum Regret

We consider a dynamic pricing problem that involves selling a given inventory of a single product over a short, two‐period selling season. There is insufficient time to replenish inventory during this season, hence sales are made entirely from inventory. The demand for the product is a stochastic, nonincreasing function of price. We assume interval uncertainty for demand, that is, knowledge of upper and lower bounds but not a probability distribution, with no correlation between the two periods. We minimize the maximum total regret over the two periods that results from the pricing decisions. We consider a dynamic model where the decision maker chooses the price for each period contingent on the remaining inventory at the beginning of the period, and a static model where the decision maker chooses the prices for both periods at the beginning of the first period. Both models can be solved by a polynomial time algorithm that solves systems of linear inequalities. Our computational study demonstrates that the prices generated by both our models are insensitive to errors in estimating the demand intervals. Our dynamic model outperforms our static model and two classical approaches that do not use demand probability distributions, when evaluated by maximum regret, average relative regret, variability, and risk measures. Further, our dynamic model generates a total expected revenue which closely approximates that of a maximum expected revenue approach which requires demand probability distributions.     

A WTP‐Choice Model: Empirical Validation,Competitive and Centralized Pricing

Willingness To Pay (WTP) of customers plays an anchoring role in pricing. This study proposes a new choice model based on WTP, incorporating sequential decision making, where the products with positive utility of purchase are considered in the order of customer preference. We compare WTP‐choice model with the commonly used (multinomial) Logit model with respect to the underlying choice process, information requirement, and independence of irrelevant alternatives. Using WTP‐choice model, we find and compare equilibrium and centrally optimal prices and profits without considering inventory availability. In addition, we compare equilibrium prices and profits in two contexts: without considering inventory availability and under lost sales. One of the interesting results with WTP‐choice model is the “loose coupling” of retailers in competition; prices are not coupled but profits are. That is, each retailer should charge the monopoly price as the collection of these prices constitute an equilibrium but each retailer's profit depends on other retailers' prices. Loose coupling fails with dependence of WTPs or dependence of preference on prices. Also, we show that competition among retailers facing dependent WTPs can cause price cycles under some conditions. We consider real‐life data on sales of yogurt, ketchup, candy melt, and tuna, and check if a version of WTP‐choice model (with uniform, triangle, or shifted exponential WTP distribution), standard or mixed Logit model fits better and predicts the sales better. These empirical tests establish that WTP‐choice model compares well and should be considered as a legitimate alternative to Logit models for studying pricing for products with low price and high frequency of purchase.     

Quick Response under Competition

We consider a manufacturer serving two competing retailers that sell their products over a single selling season. The retailers place their regular orders before the season starts. In addition to this initial order, quick response (QR) provides a retailer with an additional replenishment opportunity after demand uncertainty is resolved. The manufacturer determines the unit price for QR replenishment. We characterize the retailers’ ordering, and the manufacturer's pricing decisions in equilibrium when none, only one, and both of the retailers have QR ability. We study how the profitability of the manufacturer, the retailers, and the channel depend on QR and competition. We find it may be optimal for the manufacturer to offer QR to only one of the ex ante identical retailers when demand variability is sufficiently, but not overly high. The manufacturer may also find it optimal to offer QR to both or none of the retailers, depending on demand variability. Finally, while QR ability is always attractive for a retailer when competition is ignored, we find QR may prove detrimental when its impact on competition is taken into account.     

消费者寻求多样化与厂商折扣定价竞争

在很多市场环境中，消费者喜欢尝试不同产品的特性，重复消费同一商品会产生滞留成本。本文通过构建两期动态博弈模型，研究了滞留成本对企业折扣券定价行为的影响，并与其他定价策略的市场绩效进行了比较。本文研究结果表明：（1）企业会通过折扣券奖励忠诚的消费者，即企业会对重复购买自己产品的消费者给予价格优惠，而对新消费者制定高价格；（2）在均衡中，随着滞留成本的提升，消费者剩余和社会总福利降低，企业利润上升；（3）与其他定价机制相比较，折扣券定价策略下的社会总福利较低，政策制定者应当限制此类策略的应用。     

Pricing Decisions During Inter‐Generational Product Transition

How should companies price products during an inter‐generational transition? High uncertainty in a new product introduction often leads to extreme cases of demand and supply mismatches. Pricing is an effective tool to either prevent or alleviate these problems. We study the optimal pricing decisions in the context of a product transition in which a new‐generation product replaces an old one. We formulate the dynamic pricing problem and derive the optimal prices for both the old and new products. Our analysis sheds light on the pattern of the optimal prices for the two products during the transition and on how product replacement, along with several other dynamics including substitution, external competition, scarcity, and inventory, affect the optimal prices. We also determine the optimal initial inventory for each product and discuss a heuristic method.     

Supplier competition and its impact on firm׳s sourcing strategy

Most research on firms׳ sourcing strategies assumes that wholesale prices and reliability of suppliers are exogenous. It is of our interest to study suppliers׳ competition on both wholesale price and reliability and firms׳ corresponding optimal sourcing strategy under complete information. In particular, we study a problem in which a firm procures a single product from two suppliers, taking into account suppliers׳ price and reliability differences. This motivates the suppliers to compete on these two factors. We investigate the equilibria of this supplier game and the firm׳s corresponding sourcing decisions. Our study shows that suppliers׳ reliability often plays a more important role than wholesale price in supplier competition and that maintaining high reliability and a high wholesale price is the ideal strategy for suppliers if multiple options exist. The conventional wisdom implies that low supply reliability and high demand uncertainty motivate dual-sourcing. We notice that when the suppliers׳ shared market/transportation network is often disrupted and demand uncertainty is high, suppliers׳ competition on both price and reliability may render the sole-sourcing strategy to be optimal in some cases that depend on the format of suppliers׳ cost functions. Moreover, numerical study shows that when the cost or vulnerability (to market disruptions) of one supplier increases, its profit and that of the firm may not necessarily decrease under supplier competition.     

信息不对称条件下的企业集团转移定价研究

本文研究了信息不对称条件下企业集团的转移定价决策问题,提出了歧视转移定价法。即在信息不对称条件下,当上游子企业对中间产品具有完全垄断能力时,企业集团将转移定价决策权下放给上游子企业,上游子企业根据内外部市场需求的差异,采用差别定价策略。通过与市场基础转移定价和边际成本转移定价相比较,得出歧视转移定价可以增加企业集团的整体利润。