Advance Demand Information, Price Discrimination, and Preorder Strategies

Cuihong Li School of Business, University of Connecticut, Storrs, Connecticut 06269, [email protected] Fuqiang Zhang Olin Business School, Washington University in St. Louis, St. Louis, Missouri 63130, [email protected]

his paper studies the preorder strategy that a seller may use to sell a perishable product in an uncertain Tmarket with heterogeneous consumers. By accepting preorders, the seller is able to obtain advance demand information for inventory planning and price discriminate the consumers. Given the preorder option, the consumers react strategically by optimizing the timing of purchase. We find that accurate demand information may improve the availability of the product, which undermines the seller’s ability to charge a high preorder price. As a result, advance demand information may hurt the seller’s profit due to its negative impact for the preorder season. This cautions the seller about a potential conflict between the benefits of advance demand information and price discrimination when facing strategic consumers. A common practice to contain consumers’ strategic waiting is to offer price guarantees that compensate preorder consumers in case of a later price cut. Under price guarantees, the seller will reduce price in the regular season only if the preorder demand is low; however, such advance information implies weak demand in the regular season as well. This means that the seller can no longer benefit from a high demand in the regular season. Therefore, under price guarantees, more accurate advance demand information may still hurt the seller’s profit due to its adverse impact for the regular season. We also investigate the seller’s strategy choice in such a setting (i.e., whether the preorder option should be offered and whether it should be coupled with price guarantees) and find that the answer depends on the relative sizes of the heterogeneous consumer segments. Key words: preorder; advance demand information; price discrimination; strategic consumer behavior; price guarantee History: Received: September 10, 2010; accepted: March 22, 2012. Published online in Articles in Advance September 4, 2012.

1. Introduction The preorder option is clearly beneficial to con- Preorder refers to the practice of a seller accepting sumers because it guarantees prompt delivery on customer orders before a product is released. Such a release. This is especially valuable when the product practice has become commonplace for a wide vari- is a big hit and will be hard to find in stores due ety of products in recent years. Consumer electronic to its popularity. It is not uncommon for extremely products are among the categories for which pre- popular gadgets to run out of stock immediately after orders are often used. To name a few examples: release. Consumers may have to wait for weeks or In 2002, Apple reported the successful use of pre- even months to get the product. For instance, retail- orders for both the original and new iMac computers warned customers in mid-2006 that no Wii units ers, which revived the fortunes of the then-troubled would be available without a preorder until 2007 company (Wall Street Journal 2002). When launching (Martin 2006). Apple sold out its preorder inventory the new iPhone 3G S, the third generation of the for iPad before the release of the product (Berndtson smart phone, Apple allowed customers to preorder 2010). Preorders are often placed by enthusiastic con- the product to secure the delivery on the release sumers who are eager to be the first to get their hands

Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. date (Keizer 2009). In early September 2009, Nokia on a new product. announced that its first Linux-based smart phone, the The preorder strategy may bring significant bene- N900, was available through preorders in the U.S. fits to the seller as well. First, the seller can gauge market (Goldstein 2009). Amazon offered the pre- how much demand there will be for his product from order option to consumers when unveiling the second the preorder sales. For new products with relatively version of its e-book reader, Kindle 2 (Carnoy 2009). short life cycles, the demand is usually hard to pre- Game consoles, such as Nintendo’s Wii and Sony’s dict, yet matching supply with demand is important. Playstation 3, had been put on preorder before they Thus, the advance demand information obtained from were formally released (Martin 2006, Macarthy 2007). preorder sales will be very useful in procurement,

production, and inventory planning. The use of pre- strategy by developing a modeling framework that orders has been further promoted by the advent of incorporates all the important elements mentioned the Internet and other information technologies that above: the seller’s inventory and pricing decisions, have greatly reduced the costs associated with data advance demand information, and consumers’ strate- collection and processing. It has been reported that gic response. Speciﬁcally, we aim to address the fol- by accepting preorders for iPhone 3G S, Apple did lowing research questions: not experience the same kind of stockout problems What is the value of advance demand information? From that occurred with its iPhone 3G due to a mismatch the operations point of view, a major beneﬁt of accept- between supply and demand (Keizer 2009). ing preorders is that the seller can obtain advance Second, the preorder strategy provides leverage for demand information. This information helps improve the seller to charge different prices based on the tim- the seller’s decision on initial production runs to sat- ing of a customer’s purchase. By accepting preorders, isfy demand, and its effectiveness has been frequently the seller can identify the consumer segment that is lauded in the literature. However, a better match willing to pay a premium price for guaranteed early between supply and demand implies that availability delivery. These consumers are either new technol- of the product becomes less of a concern, which may ogy lovers or simply loyal fans of the brand. They affect consumers’ willingness to pay for a preorder. are often referred to as “early adopters,” and the Thus, it would be interesting to study when advance extra price they pay is called an “early adopter tax.” demand information is valuable to the seller in the In fact, recently the early adopter tax has received presence of strategic consumer behavior. many discussions in various industries (see Nair 2007 What is the impact of price guarantees? Consumers for video games; Jack 2007 for Apple’s iPhone; and may be reluctant to place preorders if they expect a Falcon 2009 for Sony’s latest gaming gadget, PSP possible price cut in the future. To encourage early Go). These discussions are corroborated by the obser- purchases, the seller may offer a price guarantee along vation that many products on preorder exhibit pat- with the preorder option. That is, a customer would terns of price cutting. For example, Nokia started receive a refund if the price declines over time. Price accepting preorders for its N900 smart phone at $649 guarantee has become a common industry practice and then slashed the price to $589 when it was during the past decade (Lai et al. 2010). This raises close to release (Goldstein 2009, King 2009). Walmart the question of how price guarantees affect the value dropped the preorder price of myTouch 3G Slide of advance demand information. from $199.99 to $129.99 shortly before the release When and how should a seller use the preorder strategy? (Tenerowicz 2010). Amazon charged a preorder price A seller may choose to use or not to use the preorder of $359 for its Kindle 2 and then dropped the price strategy. For example, Apple adopted the preorder to $299 after the release (Carnoy 2009). Not surpris- strategy for its iMac computers and iPhone 3G S, but ingly, consumers and market analysts may anticipate not for its iPhone 3G. Furthermore, when a preorder such price reductions and make purchasing decisions strategy is used, the seller may choose to offer or not accordingly. See Coursey (2010) and Tofel (2010) for to offer the price guarantee. When and how to use market conjectures about the iPad’s price drop even the preorder strategy is an important question for the before it is released. seller. With the preorder option, a forward-looking cus- The rest of this paper is organized as follows. tomer will choose the timing of purchase: Placing a Section 2 reviews the related literature. Section 3 preorder guarantees the availability of the product, introduces the model setting. Section 4 presents the but this is probably at the expense of a higher price; analysis of the preorder strategy. Section 5 studies waiting for a lowered price (e.g., after the product is the impact of price guarantees. Section 6 compares released) sounds quite attractive, but meanwhile the the preorder strategy and the no-preorder strategy. consumer has to face the risk of stockout. How much Sections 7 discusses several extensions of the basic a consumer is willing to pay for a preorder depends model. Section 8 concludes the paper. All proofs are on her valuation of the product and the expecta- given in Online Appendix A (provided in the electronic companion; http://dx.doi.org/10.1287/msom

Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. tion of future price and availability of the product. The seller needs to base inventory and pricing deci- .1120.0398). sions on the presence of advance demand information and consumers’ strategic behavior. Despite the 2. Literature Review prevalence of the preorder practice, there has been This paper is related to the literature on inventory surprisingly little research that analyzes the seller’s planning with advance demand information. Fisher optimal decisions while taking both demand informa- and Raman (1996) propose a quick-response strategy tion updating and forward-looking consumers explic- under which a retailer utilizes early sales for estimat- itly into account. In this paper, we study the preorder ing demand distribution. Eppen and Iyer (1997) study Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS 59

a fashion-buying problem for retailers who can divert demand information, and we study the interplay inventory to outlet stores using updated demand between these two forces. information. Gallego and Özer (2001, 2003), Özer There has been a growing interest in studying the (2003), and Özer and Wei (2004) study inventory man- impact of strategic consumer behavior on a seller’s agement with advance demand information obtained inventory decision (e.g., Su and Zhang 2008, 2009). from customer orders that are placed in advance of Cachon and Swinney (2009) and Swinney (2011) their needs. In these papers, the advance demand examine the quick-response strategy that allows the information is free and exogenously available. seller to replenish inventory after the selling season When the seller faces price-sensitive customers, starts. They focus on the value of a late ordering advance demand information becomes an endoge- opportunity (after demand is realized), whereas we nous outcome of pricing. Tang et al. (2004) and investigate the value of an early selling opportunity McCardle et al. (2004) study the benefits of an (before inventory is ordered). Cachon and Swinney advance booking discount program by which a (2009) find that early demand information is more retailer offers a price discount to consumers who valuable under strategic consumer behavior, which is make early order commitments prior to the selling in contrast with our findings. There is a key difference season. Boyacı and Özer (2010) investigate the capac- between these two papers: In Cachon and Swinney ity planning strategy for a seller who collects pur- (2009), consumers may wait for a clearance sale, the chasing commitments of price-sensitive customers. probability of which is lower if the seller can better In these papers, the advance demand is realized based match supply with demand using advance demand on an aggregate demand function. Similar to these information; in our model, consumers may wait for papers, we also consider the dependence between a price cut in the regular season after preorder sales, advance demand information and pricing. However, and the product availability in regular selling is higher we differ in that we model consumers’ strategic when more advance demand information is obtained purchasing decisions explicitly. Because of strategic from preorder sales. Swinney (2011) shows that quick waiting of consumers, we show that more accurate response may hurt a seller’s profit when consumers advance demand information does not necessarily face uncertain product valuations. We establish a par- benefit the seller. allel result that advance demand information may Existing papers that study advance selling with be detrimental to a seller’s profit, which does not strategic consumers typically consider the situations depend on value uncertainty of the product. Huang where consumers have uncertain value (or demand) and Van Mieghem (2009) study the value of online about the product or service (e.g., sport event tickets, click tracking, which allows a seller to collect advance books, videos, computer games, etc.) when making demand information for pricing and inventory plan- advance purchases. In these papers, value uncertainty ning. In their model, because clicking is separated causes price discounts for advance selling (an excep- from purchasing, advance demand information from tion is Xie and Shugan 2001, who show that a pre- click tracking always benefits the seller. mium advance-selling price may be possible when the This paper is related to the literature that stud- capacity is relatively small). This line of research often ies the use of price guarantees in intertemporal pric- assumes that the product quantity (service capacity) is ing. Png (1991) is one of the first to study the fixed, and models advance selling as a tool to increase impact of offering most-favored-customer protection market participation (e.g., Xie and Shugan 2001, Yu (i.e., price guarantee) in a two-period pricing prob- et al. 2007, Alexandrov and Lariviere 2012) or segment lem. In Png’s model, a seller wishes to sell a fixed the market (e.g., Dana 1998, Chu and Zhang 2011). inventory to two types of consumers. The size of the Zhao and Stecke (2010) and Prasad et al. (2011) con- total consumer pool is fixed, but the relative sizes sider a newsvendor retailer who uses advance selling of the two types are uncertain (so there is a per- to obtain advance demand information. Differently fect negative correlation between the demand seg- from the above studies, we focus on the situations in ments). We differ from Png (1991) in important ways: which consumers face relatively certain product value First, we endogenize the seller’s inventory decision,

Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. but uncertain product availability. This is plausible which takes the preorder sales as an input. Second, for consumer electronic goods, for which there is usu- we study the effect of advance demand information ally sufficient information for consumers to evaluate by allowing general correlation between demand seg- the product before its release, but short product life ments. Lai et al. (2010) examine the value of using cycles and unpredictable market make it difficult to price guarantees for a newsvendor seller who has match supply with demand. In this case, consumers the opportunity to mark down the product at the are willing to pay a premium preorder price to secure end of the selling season. In their problem, the seller product availability. In our model, preorder is driven determines the inventory before accepting consumer by both benefits of premium profits and advance orders; therefore, they do not include the element of Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies 60 Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS

advance demand information. Levin et al. (2007) ana- and examine the robustness of our results. Because lyze a dynamic pricing problem with ﬁxed capac- early adopters value being among the ﬁrst to own

ity and price guarantees. They focus on determining the product, we assume that the valuation vH will the optimal dynamic price and guarantee policies by be discounted by a factor ≤ 1 if a high-type con- assuming myopic consumers. sumer chooses to wait and purchase the product in Finally, dynamic pricing problems have been the second period; that is, a high-type consumer’s val- widely studied in the revenue management litera- uation becomes vH in the second period. We assume ture. The objective of these studies is to find the opti- vH > vL. All players are risk neutral and forward mal pricing and capacity (inventory) allocation rules looking, i.e., the seller aims to optimize his total to maximize a seller’s revenue/profit. Elmaghraby expected profit, and the consumers maximize their and Keskinocak (2003) and Talluri and van Ryzin expected net utility. (2004) provide comprehensive reviews of these stud- Market demand is uncertain in both periods. Let ies. Recently, there have been an increasing num- Xi denote the demand of type i (i = H1 L), where ber of papers that incorporate consumers’ strategic Xi follows a normal distribution êi (density i) with response to a seller’s pricing or capacity decisions; mean i and standard deviation i. Let i = i/i see, for example, Su (2007), Aviv and Pazgal (2008), be the ratio between the mean and standard devi- Elmaghraby et al. (2008), Liu and van Ryzin (2008), ation of Xi (i.e., the reciprocal of the coefficient of Yin et al. (2009), Levin et al. (2009), Jerath et al. (2009), variation). Bivariate normal distribution has been and Mersereau and Zhang (2012). The contribution of commonly used in the literature, especially when our paper is to consider the capacity decision along modeling demand information updating (see, e.g., with demand updating in a dynamic pricing problem, Fisher and Raman 1996, Tang et al. 2004). Let ∈ which, to the best of our knowledge, has not yet been 4−11 15 be the correlation coefficient between XH and addressed. XL. A positive correlation corresponds to situations where the primary uncertainty is on the total size of the market but not on the portion of each market seg- 3. Model ment, whereas a negative correlation relates to situa- A seller sells a perishable product in a two-period tions where the total size of the market is relatively time horizon. The product is released at the beginning certain, but the relative sizes of the two demand types of the second period (i.e., the regular selling season), are uncertain. For ease of exposition, we will focus on but the seller may accept preorders in the first period ≥ 0 in this paper; the analysis of the case < 0 is (i.e., the preorder season). There are two types of con- similar and will be discussed in §7.1. We may view sumers in the market: The high type has a valuation as an indicator of the accuracy of advance demand vH and the low type has a valuation vL for the prod- information. That is, a larger means less uncertainty uct, where vH > vL. For instance, the high type may in the second-period demand with the observation

refer to technology-savvy consumers. The difference of the ﬁrst-period demand. Deﬁne X ≡ 4XH − H 5/H , between these two valuations may represent the high- which follows the standard normal distribution; let type consumers’ stronger preference over the product ê () denote the distribution (density) function for technology; or, it may be interpreted as the addi- the standard normal distribution. We will work with

tional psychological value a technology-savvy con- X instead of XH due to their one-to-one relation- sumer obtains from owning the product (Darlin 2010). ship. For a given realization x of X, the updated ˜ Product valuation is deterministic, which means that low-type demand XL4x5 follows a normal distribution there is sufficient information for consumers to eval- with mean ˜ L4x5 = L + Lx and standard deviation p 2 uate the product before its release. This is typically ˜L = L 1 − . the case for consumer electronic products. Many firms We first describe the seller’s problem. The seller

nowadays use exhibitions, advertising, and their web- sets a preorder price p1 in the ﬁrst period. Given this sites to offer demonstration and detailed product price, the high-type consumers make their preorder information to consumers, and comprehensive prod- decisions. After the number of preorders q is received, uct reviews can often be found in professional media Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. the seller decides the second-period price p2 and the columns before the release. Consumers are inﬁnites- total production/order quantity q +Q, where Q is the imal, as widely assumed in the literature. Usually, quantity used to satisfy the second-period demand.

the technology-savvy consumers are early adopters There is a constant unit cost c (c < vL) for the product. who follow the market trend closely. Therefore, we Unsold products at the end of the second period have assume all the high-type consumers arrive in the ﬁrst negligible salvage value, and there is no penalty for period whereas all the low-type consumers arrive in unsatisﬁed demand. Thus, in the second period the the second period (see Moe and Fader 2002 for a seller essentially faces a newsvendor problem with similar assumption). In §7 we relax this assumption pricing. Note that the seller observes the preorder Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS 61

−1 quantity and may use this information to update his Define zL ≡ ê 44vL − c5/vL5, where ê4zL5 is the criti- belief about the second-period demand when making cal fractile for the low-type demand. Then the optimal the quantity decision. order quantity for the second period is given by Next we describe the consumers’ problem. The = ˜ + ˜ problem for a low-type consumer is trivial: As she Q4x5 L4x5 zLL1 (1) p arrives in the second period, she buys the product if where ˜ 4x5 = + x and ˜ = 1 − 2 are the ≤ L L L L L and only if p2 vL. A high-type consumer, arriving in mean and standard deviation of the updated low-type the first period, needs to decide whether she should ˜ demand XL4x5 for x ≡ 4xH − H 5/H . The resulting place a preorder or delay the purchasing to the next profit for the second period is period. If she places a preorder, then she pays the p price p and will definitely receive the product; oth- 2 1 çL4x5 = 4vL − c54L + Lx5 − vL4zL5L 1 − 0 (2) erwise, she may purchase the product at a possibly

lower price p2 in the regular season, but under the risk Note that the expected second-period profit is that the product is no longer available. Whether a con- Ɛ6çL4X57 = çL405 because Ɛ6X7 = 0. Throughout the sumer is willing to preorder depends on her belief of paper we use Ɛ to denote the expectation operation. the rationing risk, i.e., the chance the product will be In the first period, a high-type consumer will available in the second period. We model such a belief choose between preorder and wait. We consider sym- using a parameter ∈ 401 15: A consumer believes metric strategies for the high-type consumers because that a portion of consumers remaining in the mar- they are homogeneous. Let r denote the consumers’ ket will get the product before her. On one extreme, reservation preorder price, at which they are indiffer- = 0 means a consumer is optimistic and believes ent between preorder and wait. If a consumer pre- that she will be the first in the waiting line; on the orders at price r, then she receives a net utility vH −r; other extreme, = 1 means that the consumer is pes- if she waits, then her expected utility is 4vH − p25, simistic and thinks she will be the last in the waiting where is the consumer’s belief of the availability of line. Cachon and Swinney (2009) provide a detailed the product in the second period. By definition we discussion of this modeling approach and focus on know that vH −r = 4vH −p25 or r = vH −4vH −p25. specific values for tractability. For ease of exposi- Here we assume a consumer always preorders if there tion, we assume = 1/2 in this paper. The qualitative is a tie, because the seller can always reduce the price insights will remain if this assumption is relaxed (see by an infinitely small amount to break the tie; see Png Lemma 6 in Online Appendix A for the analysis of (1991) and Xie and Shugan (2001) for similar assump- general ). An alternative approach is to use the pro- tions. The seller must form a belief r about the con- portional rationing rule (see, e.g., Png 1991). Again, sumers’ reservation price r. Given the belief r , it is this will not change the main results as shown by the clear that the seller’s optimal price to induce preorder = extension in §7.3. is p1 r . We focus on the rational expectations (RE) equilibrium of the above game. This equilibrium con- 4. Preorder Strategy cept has been recently applied to various settings in In this section we analyze the seller’s preorder strat- the marketing and operations literatures (see Su and egy. In the analysis, we start with the seller’s price Zhang 2009 and the references therein). In any RE and quantity decisions in the second period, assum- equilibrium, the players’ beliefs must be consistent ing that all high-type consumers have chosen to pre- with the actual outcome, and the players have no order given the first-period price. Then we analyze unilateral incentives to deviate. Specifically, the equi- the seller’s first-period price decision, which induces librium requires the following conditions: (i) p1 = r ; the high-type consumers to preorder under a rational (ii) p2 = vL; (iii) the seller orders the quantity accord- expectations equilibrium. ing to (1) for the second period; (iv) r = r; and (iv) the In the second period, with the number of pre- consumer’s belief of product availability in the second orders q received in the first period, the seller must period satisfies determine the price p and the order quantity Q to sat- Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. 2 X˜ 4X5 isfy the second-period demand (besides the quantity = Ɛ Pr L < Q4X5 q to be ordered for the preorder demand). Because all 2 high-type consumers are assumed to choose preorder, L + X = Ɛ ê p + 2zL 1 (3) the number of preorders is equal to the high-type 1 − 2 demand, q = xH , and only the low-type consumers are ˜ present in the second period. Thus, it is optimal for where the second equality is by plugging XL4x5 and the seller to set p2 = vL. The seller’s order quantity Q4x5 into the first expression. Among these condi- Q depends on the high-type demand realization xH . tions, (i), (ii), and (iii) state that the seller chooses the Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies 62 Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS

profit-maximizing decisions, whereas (iv) and (v) are greater demand uncertainty ˜L. This causes the prod- the consistency conditions (players’ beliefs are consis- uct availability to decrease in . Because the first- tent with the actual outcome). The above discussion period price hinges upon the product availability, the leads to the following proposition that characterizes result in Lemma 1 implies that depending on the the equilibrium outcome of the game. problem parameters, advance demand information Proposition 1. There is a unique RE equilibrium may or may not help price discrimination in a pre- under the preorder strategy. In the equilibrium, the seller order setting. Now we are ready to analyze the influence of sets p1 = vH − 4vH − p25 and p2 = vL, where is given in (3), and all consumers will preorder in the first period. on the seller’s total profit in the preorder strategy. A higher means lower uncertainty about the For notational convenience, define ã = v − v . H L low-type demand in the second period, which helps From Proposition 1, the seller’s total expected profit improve the second-period profit. However, more is (we use superscript p for preorder strategy): accurate demand information may reduce the first- p ç = 4vH − ã − c5H + çL4051 (4) period profit at the same time: Based on Lemma 1(i), a higher may lead to greater availability in the sec- where 4v −ã −c5 is the seller’s first-period profit, H H ond period, which prevents the seller from charging and ç 405 is the second-period profit. L a high preorder price (see Proposition 1). Therefore, 4.1. Impact of Demand Correlation 45 the seller’s total profit may not necessarily increase What is the value of advance demand information in with . Define the following threshold value the preorder strategy? The accuracy of the advance v 4z 5 information can be measured by the demand corre- 45˜ ≡ − L L L (6) p 2 lation, . For the positive domain, a higher cor- 2ãzL42zL 1 − + L5 responds to more accurate advance information (i.e., the uncertainty of the low-type demand is lower after with the following property: updating). In this subsection, we investigate how the Lemma 2. (i) For zL ∈ 4−L/21 05, 45˜ increases seller’s profit depends on . p in . Based on Equation (4), the derivative of ç with (ii) For z ≤ − /2, 45˜ is quasi-convex in . respect to can be written as L L The threshold 45˜ plays a critical role in the rela- dçp d d = −ãH + çL4050 (5) tionship between the seller’s total profit and as d d d shown in the following proposition. The demand correlation affects both the first-period profit (through its influence on , the equilibrium Proposition 2. (i) If c < vL < 2c (i.e., zL < 0), then p ˜ belief of product availability in the second period) ç increases in when H < 45, and decreases in and the second-period profit ç 405. It is clear that when H ≥45 ˜ . In particular, there exists an v > 0 such p L p + 4d/d5ç 405 = v 4z 5 4/ 1 − 25 is positive—more that ç always decreases in if vL < c v. L L L L ≥ ≥ p accurate advance demand information helps the seller (ii) If vL 2c (i.e., zL 0), then ç always increases better match supply with demand, thus improving in . the second-period profit. The effect of on the first- Proposition 2 suggests that the seller’s profit period profit depends on its impact on , which is increases in only when the low-type valuation is characterized in Lemma 1. sufficiently large (vL ≥ 2c) or the high-type demand Lemma 1. (i) For c < vL < 2c (i.e., zL < 0), is is relatively small (H < 45˜ ). The intuition is as increasing in . follows: When vL is large, a greater improves (ii) For vL ≥ 2c (i.e., zL ≥ 0), is decreasing in . the second-period profit and also the preorder price. Lemma 1 suggests that the availability probability When vL is small, increasing has a negative effect may either increase or decrease in the demand corre- on the preorder price. This negative effect, however, is 1 dominated by the positive effect on the second-period lation , depending on zL. When vL < 2c, then zL < 0, profit if is low. Therefore, more accurate advance Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. and the order quantity decreases in the updated H information benefits the seller either when v is large demand variance ˜L based on Equation (1). Because L a greater reduces the variance of the updated or when H is small. demand, both the order quantity Q and its associated Figure 1 illustrates the situations in which the profit may decrease in . It draws çp as a function of product availability increase in . If vL ≥ 2c, then zL ≥ 0, and the seller will order more when facing for different H and vL values. If vL is less than 2c but not too small (−L/2 < zL < 0), 45˜ is increasing p 1 Lemma 6 in Online Appendix A studies general ∈ 401 15 and (Lemma 2(i)). Thus, ç decreases in when is rela-

identiﬁes a similar threshold structure based on the value of zL. tively low. This case is shown in the plot on the left. Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS 63

Figure 1 Impact of on the Seller’s Proﬁt in the Preorder Strategy

L = 1.02 L = 1.001 0.0050 H = 0.004 0.09 H = 0.11 0.0045

0.08 0.0040 0.003 0.08

0.07 0.0035

0.05 0.002 0.0030 0.06

0.0025 0.01 0.001 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Note. L = 5, H = 3, L = 405, vH = 2, c = 1, and = 1.

When vL is very small (zL ≤ −L/2), 45˜ is quasi- example, Apple promises to refund the difference if convex (Lemma 2(ii)). Thus, çp decreases in when price is dropped within 14 days of purchase.2 A pur- is intermediate. This case is shown in the plot on pose of price guarantee is to eliminate consumers’ the right. incentives to wait for markdowns so the seller can The above analysis delivers a message that more enjoy quicker sales at a relatively high price. Gener- accurate advance demand information (higher ) does ally, there should be some technological requirements not necessarily improve a seller’s profitability. This for implementing a price guarantee, and it might be is in contrast with the traditional wisdom that early costly to satisfy these requirements (e.g., the seller sales information (e.g., test sales, preorders) helps has to invest in hardware and manpower to monitor a firm better forecast demand and hence increase transactions and manage the refunding process). For profit (e.g., Fisher and Raman 1996). The new driv- simplicity, we assume that all necessary technologies ing force underlying our model is the counteract- are already in place and there is a zero implementa- ing effects of advance demand information and price tion cost. Under this assumption, we study the impact discrimination: Because of strategic consumer behav- of the price guarantee on the seller’s preorder strat- ior, a better ability to match supply with demand may egy. We aim to answer the following two questions: actually prevent the firm from charging premium First, when should a seller offer a price guarantee prices to extract consumer surplus. The negative effect along with the preorder option? Second, how does the of can be substantial in some situations: In the introduction of the price guarantee affect the value of extreme case where is close to 1 with a large , the advance demand information? seller has to charge a preorder price almost equal to 5.1. Value of Price Guarantee the regular-season price vL, losing the opportunity to price-discriminate different customer segments. This With a price guarantee, the seller needs to determine can lead to substantial profit loss of the seller if the not only the prices p1 and p2 in the two periods, but product value is highly diverse between the two cus- also the refund paid to each preorder consumer if = − tomer segments (large ã) or the high-type customer p2 < p1. An intuitive special case is p1 p2, which

Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. we call a full-price guarantee. Most of the existing segment is large (high H ). Practically speaking, our results imply that the preorder strategy could be less literature focuses on this special case (see, e.g., Png attractive when preorders are highly predictive of the 1991, Lai et al. 2010). Here we consider the general case without imposing any restriction on .3 Similar regular-season demand.

2 http:// store.apple.com/Catalog/US/Images/salespolicies.html (last 5. Preorder with Price Guarantee accessed August 8, 2012). Under a price guarantee, a consumer will be com- 3 We have also analyzed the full-price guarantee and obtain pensated if the product price declines over time. For similar qualitative results. In particular, the full-price guarantee Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies 64 Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS

to the preorder mechanism without price guarantee, reduces to our original preorder strategy with an

we ﬁrst analyze the seller’s decisions in the second effective preorder price p1 − . Hence, without los- period, assuming that all high-type consumers have ing generality, we restrict our attention to ≥ 4vL − c5 chosen to preorder. Then we analyze the seller’s deci- 4L/H 5. In this case, price reduction occurs only sions in the ﬁrst period that induce consumers to pre- when the preorder demand is relatively small (x < xˆ);

order under a rational expectations equilibrium. otherwise, the seller will keep the price at p1 to avoid Under a price guarantee, the second-period price is refunding the large group of preorder consumers. Our not necessarily p2 = vL because the seller may choose original preorder strategy can be considered as one to maintain a high price to avoid refunding the ear- with a price guarantee in which the refund is so low

lier buyers. At the beginning of the second period, the that the price will always be dropped, i.e., xˆ ≥ H . seller’s price decision depends on the realization of Next we analyze the seller’s first-period decision x the high-type demand in the first period, H , or equiv- on the preorder price p1 and refund . Note that the alently, x = 4xH − H 5/H . Specifically, the price will price reduction threshold, x45ˆ , depends on but not be reduced if and only if the profit from the low-type on p1. If a high-type consumer preorders, her expected consumers, ç 4x5, is greater than the total refund, L utility is u14p11 5 = vH −p1 +ê4x455ˆ ; if she waits till 4 + x5, where ç 4x5 is given in (2). Define the H H L the second period, her expected utility is u24p11 5 = breakeven level of x to be ã4ˆ x455ˆ , where ç 405 − x45ˆ ≡ L H 0 (7) ˜ − − XL4X5 H 4vL c5L 4ˆ x5ˆ ≡ Ɛ Pr < Q4X51 X < xˆ 2 Negative demand realizations from a normal distribution may cause impractical price reduction deci- L + X = Ɛ ê p + 2zL X ≤ xˆ ê4x5ˆ (8) sions. For instance, the seller may reduce the price 1 − 2 when the high-type demand is negative, because in this case the refund becomes essentially a net trans- is the probability that the product is available at the fer to the seller; or, the seller may not reduce the low price (p2 = vL) in the second period. By comparing price simply because the size of the low-type segment Equations (8) and (3), we know 4ˆ x5ˆ ≤ .

could be negative. To avoid these unrealistic scenar- Given , the optimal p1 must satisfy u14p11 5 = ios, we follow the literature (e.g., Fisher and Raman u24p11 5 so that the high-type consumers will pre- 1996) to assume hereafter the probability of negative order. This gives demand is negligible; that is, we treat Pr4XH ≤ 05 and = + ˆ − ˆ ˆ Pr4XL ≤ 0 XH 5 as zero as an approximation. It can be p145 vH ê4x455 ã4x4550 (9) shown that such an approximation is accurate in the asymptotic situation where the probability of nega- Because there is a one-to-one relationship between tive demand approaches zero (see Online Appendix A xˆ and , we will work with the decision variable for more explanation). In addition, numerical exper- xˆ instead of , which is more convenient. For any iments indicate that the qualitative insights derived given xˆ, we have 4x5ˆ = çL4x5/4ˆ H + H x5ˆ and p1 under this approximation will hold when the coefﬁ- given by Equation (9). Thus, the seller’s proﬁt can be written as (we use the superscript g for price cient of variation is reasonably small (i reasonably large).4 Lemma 3 reveals how the price reduction guarantee): decision depends on the refund and high-type g ˆ = ˆ − demand realization x. ç 4x5 4p14x5 c5H + Ɛ6ç 4X5 − 4x54ˆ + X5 X < x7ê4ˆ x5ˆ Lemma 3. (i) If ≤ 4vL − c54L/H 5, then price L H H reduction will always happen. ˆ = 4vH − ã4x5ˆ − c5H (ii) If > 4vL − c54L/H 5, then price reduction hap- pens when x < x45ˆ , and x45ˆ decreases in . + Ɛ6çL4X5 − 4x5ˆ H X X < x7ê4ˆ x50ˆ (10)

For < 4vL − c54L/H 5, the seller will always When should the seller provide a price guaran- reduce the price regardless of x to benefit from tee? We may compare the seller’s profits under the Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. serving the low-type consumers. This case essentially preorder strategy with and without price guarantee. From (10), the profit margin from the high-type con- performs very close to optimal. More details can be found sumers in the price guarantee mechanism is vH − in Online Appendix B (available in the electronic companion; ã4ˆ x5ˆ − c, which is greater than the one without a http://dx.doi.org/10.1287/msom.1120.0398). price guarantee, v − ã − c. This is true because a 4 For example, with = 3 and = 4, the probability of a negative H H L price guarantee enables the seller to charge a higher XH is only 000014 and the conditional probability of a negative XL is at most 00004. The main insights hold in this example, even without preorder price by discouraging consumers from wait- the approximation. ing. Such an observation suggests that offering a price Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS 65

guarantee will be more effective if the size of the does the opposite. Therefore, as shown in Lemma 4(i), high-type consumers is larger. Indeed, Proposition 3 ˆ may decrease (thus the preorder price may increase) g g conﬁrms this intuition. We use ç = max ç 45 to in when is small. This is in contrast to the result denote the seller’s optimal proﬁt in the price guaran- without a price guarantee that is always increasing

tee mechanism. in for zL < 0. When zL ≥ 0, under the assumption that the probability of negative demand is negligible, Proposition 3. Suppose H is fixed. Then there exists g g p it can be shown that the second-period product avail- a ˆ H such that ç > ç (i.e., the seller should offer a price guarantee in the preorder strategy) if and only if > ˆ g . ability upon price reduction is one, independent of . H H ˆ Thus, (and ) is independent of for zL ≥ 0, as Proposition 3 suggests that a price guarantee is ben- shown in Lemma 4(ii). eficial to the seller only when H is above a thresh- g g Because the influence of on the product avail- old value, ˆ H (a closed-form expression of ˆ H can be ability applies only when there is a price reduction, found in the proof). In other words, the size of the a price guarantee will mitigate the negative effect of high-type consumer segment must be large enough on the preorder price. Furthermore, the price guar- to warrant the use of price guarantees; otherwise, the antee may even reverse the effect when is small, as seller should not offer a price guarantee. Two points suggested by Lemma 4(i). However, in the meantime are worth mentioning about this threshold result: the price guarantee prevents the seller from serving a First, fixing H implies that the standard deviation large low-type segment, because the price is reduced of the high-type demand changes proportionally with to target the low-type segment only when the seg- the mean. We find from numerical analysis that a sim- ment is relatively small. This implies that the price ilar result holds when H , rather than H , is fixed. guarantee introduces an adverse effect of on the That is, the result can be extended to settings with second-period profit. To better understand the impact a fixed standard deviation. Second, the threshold ˆ g H of on the seller’s total profit, we focus on two spe- depends on the relative sizes of the two consumer cial cases: the case when v is small (close to c) and segments. Analogously, it can be shown that for a L g the case when vL is large (greater than 2c). When vL is fixed L, there is a threshold ˆ L such that the price g very small, the second-period profit is negligible, and guarantee is preferred if and only if < ˆ . This L L the effect of focuses on the price and profit in the is the counterpart of Proposition 3 and is therefore preorder period. When v ≥ 2c, the product availabil- omitted. L ity in the second period (conditional on a price reduc- 5.2. Impact of Under Price Guarantee tion) is independent of according to Lemma 4(ii); We have shown in §4.1 that a higher may decrease thus, the effect of is primarily on the second-period the seller’s profit in the preorder strategy because of profit. the strategic waiting behavior. The underlying reason Proposition 4. (i) There exists 1 11 2 > 0 such is that when zL < 0, a higher improves the product g that, if vL − c < , then dç /d > 0 for = 0 and availability in the second period, and thus the seller g g dç /d < 0 for > 1 − 1, with dˆ H /d < 0 for = 0 has to charge a lower preorder price. How does this g and dˆ H /d > 0 for > 1 − 2. result change when price guarantees are used? Here g (ii) When vL ≥ 2c (i.e., zL ≥ 0), ç is quasi-convex we investigate the impact of under price guarantees. g ( first decreasing and then increasing) in ; in addition, ˆ As an intermediate result, Lemma 4 reveals the effect H is increasing in . of on the probability that the product is available at ˆ the low price in the second period, . When vL is very small, we know from Proposi- tion 2(i) that the seller’s profit without price guarantee Lemma 4. (i) For c < v < 2c (i.e., z < 0) and a given L L always decreases in . With a price guarantee, how- xˆ, d/ˆ d ≤ 0 at = 0, and there exists > 0 such that ever, Proposition 4(i) shows that the seller’s profit is d/ˆ d ≥ 0 for ≥ 1 − . increasing in for close to 0, and decreasing in ≥ ≥ ˆ ˆ ˆ = ˆ (ii) For vL 2c (i.e., zL 0) and a given x, 4x5 ê4x5 for close to 1. Through numerical experiments, we is independent of . observe that çg is quasi-concave over ∈ 601 15. This Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. Recall from Lemma 3 that a price reduction occurs difference results from the fact that the price guaran- only when the high-type demand is relatively low tee mitigates and may even reverse the negative effect (x < xˆ), which indicates a weak low-type demand as of on the preorder price, especially when is small. g well. Therefore, in case of a price reduction, a higher Proposition 4(ii) also indicates that ˆ H decreases in implies both smaller mean and variance for the when is close to 0, and increases in when is updated low-type demand. Whereas the effect on the close to 1. Again, we observe from numerical exper- g variance drives the second-period product availabil- iments that ˆ H is quasi-convex over ∈ 601 15. Thus, ity to increase in with zL < 0, the effect on the mean when vL is small, price guarantees are favored only Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies 66 Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS

for intermediate ; when is either high or low, the superscript n stands for no preorder. In the RE equi- preorder strategy without price guarantee is better. librium, for a given Q, the first-stage price satisfies When v ≥ 2c, recall from Proposition 2(ii) that L n the seller’s profit without price guarantee is always p14Q5 = vH − ã 4Q50 (12) increasing in . Interestingly, Proposition 4(ii) shows Given Q and p , the seller’s total profit is that, with the optimal price guarantee, the seller’s 1 profit may be decreasing in for sufficiently small . n ç 4p11 Q5 = 4p1 − vL5 Ɛ6min4Q1 XH 57 That is, more accurate advance demand information + + − may hurt the seller’s profit under price guarantees vL Ɛ6min4Q1 XH XL57 cQ0 even when it would only benefit the seller without The seller’s optimal order quantity Qn is given by a price guarantee. This result is due to the negative n the first-order condition 4¡/¡Q5ç 4p11 Q5 = 0 for p1 effect of on the second-period profit introduced by defined in (12). The seller’s total profit in equilibrium the price guarantee. In comparison, note that without can be written as price guarantee, the negative effect of is realized n n n n only on the first-period profit. ç = ã41 − 4Q 55 Ɛ6min4Q 1 XH 57 From Proposition 3, the seller prefers to use a price n n g + vL Ɛ6min4Q 1 XH + XL57 − cQ 1 (13) guarantee when H > ˆ H . Proposition 4(ii) suggests ≥ that, for vL 2c, the seller is less likely to use a where ã41 − n4Qn55 represents the premium margin price guarantee as increases. This is again due to from the high-type consumers. the adverse effect of a higher on the second-period We may compare the seller’s profit in Equation (13) profit. Such an effect is substantial for large vL, mak- to that under the preorder strategy in Equation (4), ing price guarantees less attractive as increases. which leads to the following result. n Proposition 5. Suppose H is fixed. There exists a ˆ H 6. No-Preorder Strategy such that çp > çn (i.e., the seller prefers the preorder strat- When should the seller offer the preorder option? In n egy over the no-preorder strategy) if and only if H < ˆ . this section, we compare the preorder strategy with H the no-preorder strategy. With no preorder, the prod- Proposition 5 states that the preorder strategy uct is sold only in the regular selling season (i.e., after should be used if and only if the size of the high-type n the product is released). As a result, the seller does not demand is less than a threshold value, ˆ H . Through have advance demand information when deciding the numerical experiments we find that a similar thresh- order quantity. In this case, the seller may charge a old value exists when H , rather than H , is fixed. high price to target the high-type consumers first, and Thus, we conclude that the preorder strategy out- then drop the price to satisfy the low-type consumers performs the no-preorder strategy when the relative if there is still inventory left. For ease of exposition, size of the high-type customers is smaller than a we divide the regular season into two stages, and certain threshold. The intuition can be explained as follows. Without advance demand information, the let p1 and p2 (p1 ≥ p2) denote the prices in the two stages (we use “stage” to distinguish from the notion future product availability tends to be lower, thus of “period” used in the previous sections). Below we raising a high-type consumer’s willingness to pay at study the game under no preorder and then compare the beginning. With a greater profit margin from the the three strategies we have examined so far. Again, high-type consumers, the no-preorder strategy bene- we analyze the equilibrium in which all high-type fits more from the expansion of the high-type demand consumers purchase in the first stage; in this equilib- segment than the preorder strategy. It can be shown p n rium, the second-stage price p is set to v to target that both ç and ç are linearly increasing in H (for 2 L ˆ n the low-type consumers. As in the previous models, fixed H ). Thus, the search of H is straightforward, if a high-type consumer waits to purchase in the sec- as shown in the proof of the proposition. Thus far we have studied three different strategies: ond stage, the product value is discounted to vH for the loss of early-adopter advantages. no preorder, preorder, and preorder with price guar-

Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. Let the seller’s order quantity be Q. If a high-type antee. The threshold values in Propositions 3 and 5 consumer delays purchasing to the second stage, she may help the seller make pairwise comparisons of faces the availability probability the strategies. However, ranking all three strategy choices is difﬁcult. Hence, we rely on an extensive Q − numerical study to obtain some insights. We report n4Q5 = Pr4X + X < Q5 = ê a 1 (11) H L two main observations from the numerical analysis. a First, as H increases, the seller’s optimal strategy p 2 2 2 where a = H + L and a = H + L + 2LH shifts from preorder to no preorder and then to pre- are the mean and standard deviation of XH +XL. The order with price guarantee. Second, the range for the Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS 67

p g n Figure 2 Comparison of ç , ç , and ç for Different H and vL Values = 1.05 L = 1.01 L 0.30 0.06 Π p 0.28 Π g

n Π 0.26 0.05 0.24

0.22 0.04 0.20

0.18 0.03 0.16

0.14

0.01 0.02 0.03 0.04 0.05 0.06 0.05 0.10 0.15 0.20 0.25 0.30 H H

Note. L = 5, L = 405, H = 3, vH = 2, c = 1, and = 1.

no-preorder strategy to stand out may degenerate to highly profitable. Therefore, for large enough vL, the zero, especially when vL is large. Figure 2 shows a seller should always accept preorders, either with or representative example, where the left plot illustrates without a price guarantee. the first observation and the right plot shows the second observation. Here is the intuition behind these observations: 7. Extensions Based on Proposition 5, we know the preorder strat- The basic model studied in the previous sections is built on some assumptions that help maintain ana- egy dominates the no-preorder strategy when H n lytical tractability and reveal the key driving forces is relatively small (H < ˆ H ). From Proposition 3, we know the price guarantee strategy outperforms underlying the results. This section relaxes some of the assumptions and discusses their implications to the preorder strategy when H is relatively large g the analysis and results. (H > ˆ H ). Therefore, the preorder strategy is optimal among the three when H is sufficiently small n g 7.1. Negative Demand Correlation 4 < 05 (H < min4ˆ H 1 ˆ H 5). Now we focus on the comparison between the no-preorder strategy and the price So far we have focused on ≥ 0 in the analysis. This guarantee strategy. In the no-preorder strategy, the is appropriate when modeling new product introduc- profit margin from the high-type consumers is inde- tions, of which the total market size is variable and each consumer segment expands with the total mar- pendent of H . In the price guarantee strategy, by contrast, the profit margin from the high-type consumers ket. There may be situations where the total market size is relatively certain, but the portion of each con- is increasing in H : Because of the refund liability, the seller is less likely to reduce the price when facing a sumer segment is variable. These situations can be captured by a negative demand correlation (see, for larger H ; this reduces a high-type consumer’s incen- tive to wait, leading to a higher preorder price. Hence, example, a model with = −1 in Png 1991). For com- under the price guarantee strategy, the profit margin pleteness, here we provide a brief discussion of neg- from the high-type consumers will be higher than that ative demand correlation. With a negative , a small (thus a large ) Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. in the no-preorder strategy when H is sufficiently large. This suggests that the price guarantee strat- means more accurate advance information. A nega-

egy dominates the no-preorder strategy for large H . tive does not change the analysis of the preorder Thus, the no-preorder strategy can only stand out strategy without price guarantee in §4. By replacing

for intermediate H . However, such a range may with −, it can be readily shown that all results in degenerate to zero when vL is large for the following §4 apply to ∈ 4−11 07 as well. Next we discuss the reason. With a large vL, the advance demand infor- preorder strategy with price guarantee. mation obtained from the preorder sales will be more Under a price guarantee, the seller will lower the valuable because selling to the low-type consumers is price in the second period if and only if the realized Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies 68 Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS

high-type demand is less than a threshold. In contrast consumers to arrive in the preorder season (1 − is

to the case of positive , now < 0 means that price the fraction in the regular season). We use X1H = reduction occurs when the low-type demand is rela- XH and X2H = 41 − 5XH to denote the high-type tively high. That is, as increases, the variance of demand in the preorder and regular seasons, respec- the low-type demand under price reduction becomes tively. Let the correlation coefficient between X1H and smaller, whereas the mean becomes stochastically XL be . Thus, the seller can update his belief about larger. Therefore, under a negative demand correla- both the low-type demand and second-period high- tion, the negative effect of advance information intro- type demand after observing X1H : Given a realization duced by price guarantees on the second-period profit x1H = 1H + 1H x, the updated distribution of XeL will does not exist anymore. have a mean ˜ L4x5 = L + Lx and standard devia- p 2 Although < 0 removes the negative impact of tion ˜L = L 1 − , and the high-type demand in the increasing on the second-period profit, interest- regular season will be x˜2H 4x5 = 41/ − 15x1H . We fur- ingly, it aggravates the negative effect on the first- ther assume = 1 in this extension. The rest of the period profit. This is because, with a higher , the model setting is the same as before. Our basic model low-type demand in case of price reduction tends to represents a special case with = 1. The purpose of be larger, which motivates the seller to order more to this subsection is to examine whether the key insight satisfy demand in the regular season. This improves carries over from the basic model with = 1 to gen- the product availability in the regular season and eral < 1. The detailed analysis is provided in Online leads to a lower preorder price. Thus, for < 0, a Appendix A. Here we highlight the key findings. higher will have a stronger adverse impact on the First we describe the case without price guaran- preorder price under a price guarantee; as a result, tee. The seller’s decisions are as follows: In the pre- the seller’s optimal preorder price always decreases order season, the seller sets a price p1 to satisfy in . the high-type customers. Then, after observing the To summarize, with negative , all results about preorder demand X1H , she updates her belief about the preorder strategy without price guarantee remain. future demand (X2H and XL) and determines the order Under a price guarantee and < 0, a larger hurts quantity Q; meanwhile, she also sets a price p2 > vL the first-period profit (in a stronger way compared to to induce the high-type customers to purchase in ≥ 0), but always improves the second-period profit. the regular season. Finally, if there is still leftover Therefore, with < 0, we still have the result that inventory, the seller lowers the price to p3 = vL to more accurate advance demand information may hurt clear the inventory. In fact, we may view this as a seller’s profit under a price guarantee, although this a three-stage model where pi denotes the price in result is solely caused by the conflict between advance stage i (i = 11 21 3). The customers in each stage decide demand information and price discrimination. whether they want to purchase immediately or wait until the next stage. Again we focus on the rational 7.2. Mixed Arrivals expectations equilibrium under symmetric strategies It has been assumed in the basic model that the for the high-type consumers. In the equilibrium, all high-type consumers arrive in the preorder season, the high-type customers in stage 1 will preorder at whereas the low-type consumers appear in the reg- price p1, and all the high-type customers in stage 2 ular season. As a result, the regular price is always will purchase at price p2. Note that p depends on the realization of the pre- vL and lower than the preorder price. In this subsec- 2 tion we extend the basic model to consider a mixed order demand X1H , or X = 4X1H − 1H 5/1H . It can be arrival model where the high-type customers arrive shown that p1 = Ɛ6p24X57; thus, depending on the real- in both periods. For simplicity, we still assume that all ization of X, both p1 > p2 and p1 < p2 may happen: If the low-type consumers show up in the regular sell- the realization of X is low, then the product availabil- ing season.5 Let ( ≤ 1) be the fraction of high-type ity in stage 3 will be low, and this allows the seller to charge a high price p2 in stage 2; the opposite is true when the realization of X is high. Therefore, for 5 A more general model is to allow some low-type consumers in the

Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. the more general setting, we may observe a preorder preorder season as well. However, this will not change the analysis as long as the preorder sales target the high-type customers price that is either higher (i.e., a premium preorder only. In this case, the low-type consumers will wait to purchase price) or lower (i.e., a discount preorder price) than the product in the regular season. For fashion and innovative prod- the regular price. In the advance selling (preorder) lit- ucts, the high-type consumers usually dominate in the preorder erature, a discount advance selling price is attributed season whereas the low-type consumers dominate in the regular to the uncertainty in product valuation, whereas we season, and they differ substantially in their willingness to pay. It is unlikely the seller sets a low price to satisfy both types of con- have shown that a discount preorder price is possible sumers in the preorder season. Therefore, we focus on the situation even without valuation uncertainty. Despite the more where the preorder sales target the high-type consumers only. complex pricing patterns, our result about the impact Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS 69

of remains unchanged as shown in the next propo- experiments, we find that its expectation Ɛ6pr 4X57 is sition. That is, the adverse effect of advance demand always increasing in . This implies that under the information on the seller’s profit does not rely on a proportional rationing, again, more advance demand premium preorder price. Instead, it only hinges upon information leads to a lower preorder price in the pre- the possibility that the product may be available at order strategy. a future low price, no matter when the price will be In the price guarantee mechanism, for a given price dropped (it can be after the product release). reduction threshold xˆ < 0, the probability that the = Proposition 6. Consider the mixed arrival model. If product is available at the low price (p2 vL) in the pr pr p second period is ˆ 4x5ˆ = Ɛ6 4x5 x ≤ x7ê4ˆ x5ˆ . From zL < 0, there exists a ˜ such that ç increases in if and p Lemma 5, ˆpr 4x5ˆ is decreasing in if < −x/ˆ ; this only if 1H ≤ ˜ . If zL ≥ 0, then ç always increases in . L suggests that the negative effect of advance demand Next we consider the case with price guarantee. information on the preorder price may be reversed The analysis for mixed arrivals is more involved with a price guarantee when is small. because the seller needs to set multiple prices and The above results indicate that advance demand refunds. To simplify analysis, we assume that for any information has a similar effect on the seller’s first- customer, the refund is based on the purchasing price period profit with or without price guarantee as and the final price of the product. There are two pos- under the -rationing rule. Note that the choice of sible final prices in stage 3: vL if the seller lowers the the rationing rule does not affect the seller’s second- price to satisfy the low-type customers, or vH if the period profit. Therefore, the main results about the seller does not serve the low-type customers at all. effect of on the seller’s overall profit continue to The seller needs to determine two refunds 1 and 2 hold under the proportional rationing rule. in stages 1 and 2, respectively, where 1 is the refund to the preorder customers in stage 1 and 2 is the refund to the high-type customers in stage 2, if the 8. Conclusion final price is reduced to vL. This paper studies the prevailing preorder practice Again, we find that even under price guarantees, in which a seller accepts consumer orders before the seller’s total profit may decrease with in certain the release of a product. Consumers who are eager circumstances. In particular, the price guarantee miti- to obtain the product will benefit from preorder gates the negative effect of on the margin from the because it guarantees immediate product availabil- high-type customers, but it introduces a new negative ity on release. Preorder is also beneficial to the seller effect of on the profit from the low-type customers. because it allows the seller to gauge market demand Together with Proposition 6, this finding confirms the from preorder sales, and to charge distinct prices robustness of the key insight from the basic model: to different consumer segments. In this paper, we In the preorder strategy, more accurate demand infor- develop a modeling framework to analyze the pre- mation may hurt a seller’s profit regardless of the use order strategy a seller may use to sell a perishable of price guarantees. product in a short selling season. The market con- sists of two consumer segments, those who arrive in 7.3. Proportional Rationing Rule the preorder season with valuation v and those in In this extension, we examine the robustness of our H the regular selling season with valuation v , respec- key results under the proportioning rationing rule. L tively. There is a correlation between these two ran- To facilitate discussion, we define the probability dom demand segments, which we use to measure of product availability in the second period, contin- the accuracy of advance demand information. To the gent on the preorder demand + x, to be (the H H best of our knowledge, this modeling framework is superscript pr stands for proportional rationing): the first to simultaneously incorporate the following ˜ three important elements: seller’s inventory and pric- pr min4Q4x51 XL4x55 4x5 = Ɛ 1 (14) ing decisions, consumers’ forward-looking behavior, X˜ 4x5 L and advance demand information. ˜ The value of advance demand information has Downloaded from informs.org by [128.252.111.87] on 06 March 2015, at 12:05 . For personal use only, all rights reserved. where XL4x5 is the updated low-type demand. pr been widely studied in the operations literature. Most Lemma 5. 4x5 is increasing in if and only if studies emphasize the benefit of advance demand ≥ − x L. information, i.e., it helps improve a firm’s inven- In the preorder strategy (without price guaran- tory decision when facing uncertain market demand. tee), a high-type customer’s belief of product avail- However, we find that the seller’s profit may decrease ability is given by Ɛ6pr 4X57. Lemma 5 shows that with the accuracy of advance demand informa- pr 4x5 is increasing in when the realization of high- tion obtained from the preorder sales. Specifically, type demand is large. Through extensive numerical the seller will benefit from more accurate advance Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies 70 Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS

demand information only if the low-type valuation the preorder season provides a positive signal about is sufficiently large or the high-type demand is rel- the product value). Incorporating information updat- atively small. This result is due to a possible con- ing for the consumers in addition to demand updat- flict between advance demand information and price ing for the seller is an interesting direction for future discrimination: Accurate demand information may research. Second, this paper focuses on a monopolist’s increase product availability in the regular selling selling strategy. A natural extension is to consider the period, which hinders the seller from charging a high preorder strategy in a duopoly setting. It would be price to the high-type customers in the preorder season. interesting to study how competition affects the firms’ An effective way of resolving such a conflict strategy choice and the associated pricing and inven- between advance demand information and price dis- tory decisions. crimination is to offer a price guarantee: the seller promises to compensate early purchasers in case the Electronic Companion price is lowered later. Interestingly, we find that the An electronic companion to this paper is available as part seller’s profit may still decrease in the accuracy of of the online version at http://dx.doi.org/10.1287/msom advance demand information, even when the seller .1120.0398. would benefit from more advance demand information if the price guarantee were not offered. The expla- Acknowledgments nation of this result is as follows. Although price The authors thank Laurens Debo, Stephen Gilbert, Guoming guarantees can mitigate (and in some situations may Lai, Martin Lariviere, Özalp Özer, Kathryn Stecke, and even reverse) the effect of the above conflict, they Xuying Zhao, as well as participants at the 2009 MSOM Conference in Boston, Massachusetts; the 2009 INFORMS introduce another adverse effect of advance demand Annual Meeting in San Diego, California; and the 2010 information: With price guarantees, a seller will lower MSOM Supply Chain Management SIG Conference in the price to profit from low-type consumers only Haifa, Israel, for helpful comments and discussions. The when the preorder demand is relatively low, but low authors acknowledge the financial support from the Boeing preorder demand implies weak low-type demand as Center for Technology and Informational Management and well (when the two demand segments are positively the Connecticut Information Technology Institute. correlated). As a result, the use of price guarantees excludes situations where the seller can enjoy a great profit in the regular season from low-type con- References sumers, and such an adverse effect is stronger when Alexandrov A, Lariviere MA (2012) Are reservations rec- the advance demand information is more accurate. ommended? Manufacturing Service Oper. Management 14(2): 218–230. Therefore, contrary to conventional wisdom, we Aviv Y, Pazgal A (2008) Optimal pricing of seasonal products in the have demonstrated that advance demand informa- presence of forward-looking consumers. Manufacturing Service tion can be detrimental to firms when facing forward- Oper. Management 10(3):339–359. looking consumers: (1) It may hurt the seller’s profit Berndtson C (2010) Apple sells out iPad preorder inventory as in the preorder season through its negative effect launch nears. CRN (March 29), http://www.crn.com/. on the preorder price. (2) In the presence of price Boyacı T, Özer Ö (2010) Information acquisition for capacity planning via pricing and advance selling: When to stop and act? guarantees, it can also hurt the seller’s profit in Oper. Res. 58(5):1328–1349. the regular season through its negative effect on Cachon GP, Swinney R (2009) Purchasing, pricing, and quick the regular-season demand. Because of such nega- response in the presence of strategic consumers. Management tive effects of advance demand information, the seller Sci. 55(3):497–511. needs to carefully decide whether to accept pre- Carnoy D (2009) Amazon drops price of Kindle 2 to $299. CNET (July 8), http://news.cnet.com/. orders and whether to provide price guarantees with Chu L, Zhang H (2011) Optimal preorder strategy with endogenous preorders. We find that the seller’s strategy choice information control. Management Sci. 57(6):1055–1077. depends critically on the relative market sizes of the Coursey D (2010) Apple iPad price cut: Blunder or brilliance? two types of consumers. To be specific, the preorder PCWorld (February 8), http://www.pcworld.com/. option should be used without a price guarantee if Dana J (1998) Advance-purchase discounts and price discrimination in competitive markets. J. Political Econom. 106(2):395–422.

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