Pricing Promotional Products Under Upselling

MANUFACTURING & SERVICE

Goker Aydin

.org/. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109, [email protected] ms author(s). or Serhan Ziya

.inf Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, the Chapel Hill, North Carolina 27599, [email protected] to nals

pselling is offering an additional product to a customer who just made a purchase. Most catalogers and tesy Uonline sellers, in addition to some traditional retailers, use upselling often to clear inventories of slow- moving items. We investigate the pricing and discounting questions for such an item, which we call the promo- http://jour cour tional product. In our model, an arriving customer may purchase this promotional product or one of the other at a products that the ﬁrm sells. If the customer purchases one of the other products, the promotional product is le as offered to the customer, possibly with a discount. While deciding whether to offer a discount and, if so, how

y big a discount to offer, the ﬁrm uses the information that the customer has just bought a certain product with ailab

v a certain price. We investigate how discounting decisions depend on the inventory levels, time, type of pric- a cop ing policy in use, and the relationship between the customers’ reservation prices for the promotional product is

, and the other products (negatively or positively correlated). In particular, we ﬁnd that if the ﬁrm sets prices this and discounts dynamically and the customers’ reservation prices for the promotional product are negatively correlated with their reservation prices for the product they purchased, then customers are always offered a uted

policies discount regardless of the inventory levels and time. On the other hand, if the customers’ reservation prices for ib the promotional product are positively correlated with their reservation prices for the product they purchased, then the customer may or may not be offered a discount, depending on the inventory levels and time. Our distr numerical study shows that the benefit to the firm from using customer purchase information is high when the mission firm uses a static price, but chooses discounts dynamically. We also find that although dynamic discounting and

per decisions bring modest improvements, setting the price dynamically seems to have a more significant effect on the firm’s profits. ticle and

ar Key words: dynamic pricing; pricing of limited inventories; cross-selling; bundling History: Received: June 27, 2006; accepted: June 1, 2007. Published online in Articles in Advance January 4, 2008. ights this r to 1. Introduction 1999), Corona Cigar Co., based in Ocoee, FL (Ferriolo Every time one buys a burger from a fast-food restau- 2003), toy and novelty cataloger Oriental Trading Co., including yright rant, one will be asked the famous question: “Do and apparel cataloger DM Management (Miller 1995) use upselling. Online retailers such as Amazon and cop you want fries with that?” Those who avoid burg- Buy.com also use upselling by recommending addi-

mation, ers in favor of subs will face a similar question

or after ordering a sandwich: “Do you want to add tional products to customers who just purchased an holds inf any chips or drinks?” Upselling refers to this prac- item. Traditional retailers are no strangers to the practice of offering an additional product to a customer tice either. Most people can remember being offered who just made a purchase.1 Many catalog retailers a tie that will go with their new shirt or a blouse that will be perfect with their new pants. such as Lillian Vernon, based in Rye, NY (Andrews INFORMS Additional One goal of upselling is to increase revenue per customer visit. Retailers typically try to sell each cus- 1 The practice is also called cross-selling. Because the Federal Trade tomer an additional product related to the one the Commission (FTC) deﬁnes upselling in the context of telemarket- customer just bought, e.g., offering a battery charger ing as “soliciting the purchase of goods or services following an initial transaction during a single telephone call,” we use the term to a customer who just bought a digital camera upselling instead of cross-selling. (See FTC’s Telemarketing Sales or offering a carrying case to a customer who just Rule in Code of Federal Regulations Title 16, Part 310.) ordered a cell phone. Another popular reason for the

use of upselling is liquidation of excess inventories. find it harder to do because the initial price is already In fact, according to a study by Catalog Age, 42% published in the catalog. Regardless of whether the of all catalog retailers and 63% of apparel cata- firm engages in such dynamic pricing the firm can logers use upselling to reduce excess merchandise choose to use upselling. In cases where dynamic pric- (Del Franco et al. 1999). The retailer identifies slow- ing is used, upselling can be seen as a promotional moving items with excess inventory and tries to tool that complements dynamic pricing as a means of .org/. liquidate that inventory by offering the items, possi- clearing inventory. We consider both the case in which ms bly at a discount, to customers who purchase other the firm is dynamically adjusting the announced price author(s). or items. For example, the cataloger DMManagement over time and the case in which there is a fixed price .inf the is reported to use a computerized method to identify that cannot be adjusted. to nals overstock items, which are then promoted by sales When making an upsell offer, the firm must decide representatives (Miller 1995). In this paper, we focus whether the offer should be accompanied by a dis- tesy on upselling practices aimed at liquidation of excess count from the announced price. Whether the upsell http://jour cour inventories. In particular, we assume that the firm offer will include a discount may depend on the at a has already chosen an item for upselling (hereafter, remaining inventory of the promotional product and

le the promotional product), and we focus on the pric- as the time remaining until the end of the selling season. y ing of this promotional product. Some natural choices In addition, the ﬁrm may be able to tailor the dis- ailab v

a for the promotional product would be a discontinued cop counting decisions at the individual customer level.

is product or a seasonal product with excess inventory. A ﬁrm using upselling has one valuable piece of infor- , this Whereas the inventory of the promotional product mation about the customer who is about to receive is liquidated through upselling, the products that are the upsell offer: The ﬁrm knows that this customer uted policies not subject to upselling, which we refer to as regu- has just purchased a certain product at a certain ib lar products, are likely to be staple items sold over price. This information sets this particular customer distr an extended period of time, or fast-moving seasonal apart from a random customer in the population and

mission products. Staple items are replenished regularly, and allows the ﬁrm to make a better-informed decision and

per we expect that lost sales due to stockouts will be rare on whether to offer a discount. Here we analyze the for such products. On the other hand, when the reg-

ticle beneﬁts from using such information. and ar ular product is a fast-selling seasonal product with In some cases, the ﬁrm may be able to decide not no replenishment opportunities, there is a chance that only whether the upsell offer to an individual cus- ights this r the regular product will run out of stock before the tomer should include a discount, but also how deep to promotional product does, which needs to be taken the discount should be. For example, an online retailer into account when upselling the promotional prod- could send customized coupons to individual cus-

including uct. We first consider the case in which the regular yright tomers. Likewise, a cataloger can make different dis- product has unlimited supply, so that it is available count offers to different customers while the customer cop whenever a customer demands it. We then consider is making a purchase over the phone. On the other mation, what happens when the regular product has limited hand, a firm may choose to fix the discount level (e.g., or holds

inf availability. using a coupon with a given face value) while decid- When a firm is upselling a product, in addition ing whether to offer the discount at the individual to those customers buying the product on an upsell customer level (e.g., whether to offer the coupon to a offer there will be others who arrive with the inten- given customer.) We consider both the case in which INFORMS Additional tion of purchasing the product in the first place. Such the discount level can differ across customers and the customers will observe an announced price for the case in which the discount level needs to be the same product. If the firm is trying to clear the excess inven- for all customers who get a discount.2 tory of the product, then it would be natural for the firm to adjust the announced price over time as long 2 Offering different discounts to different customers may raise ques- as it is feasible to do so. This may be quite possi- tions of legality. In the form of upselling that we investigate, the ble for an online retailer, whereas a cataloger may discount is akin to offering a discount on a bundle of products. Aydin and Ziya: Pricing Promotional Products Under Upselling 362 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

We first analyze the dynamic price, dynamic dis- 2.1. Bundling count case where the firm can dynamically adjust the The practice of upselling is closely related to bun- announced price of the promotional product as well dling, i.e., selling two or more products as one pack- as customize the discount that comes with an upsell age. One can think of upselling as a special form of offer. We show that an upsell offer will include a bundling in which the customer is given the option discount if and only if the promotional product and to purchase the bundle only after she has commit- .org/. the regular product are dissimilar, irrespective of the ted to buying a product. There is a rich literature in ms inventory status and time left until the deadline. The marketing and economics on the practice of bundling. author(s). or two products being dissimilar refers to a set of condi- For a review, see Stremersch and Tellis (2002). The .inf the tions that imply that a customer’s reservation prices research on bundling in economics literature starts to nals for the two products are negatively correlated. Like- with the work of Adams and Yellen (1976) and gen- wise, we say that two products are similar if a cus- erally focuses on the question of whether bundling tesy tomer’s reservation prices for the two products are is beneficial to the seller or the consumer population. positively correlated. When the products are similar, http://jour cour The marketing research on bundling has considered at a we show that the firm may or may not offer a dis- the same question in addition to how consumers eval-

le count, depending on the inventory levels of the regu-

as uate bundles (Yadav and Monroe 1993) and the opti- lar and promotional products. y mal pricing of bundles (Hanson and Martin 1990). ailab

v We also consider a number of extensions to the base a cop Taking a more operational perspective, given exoge- model: the case of multiple regular products; the static is nously ﬁxed bundling decisions, Ernst and Kouvelis , this price, dynamic discount case (where the announced (1999) consider the question of setting the inven- price is ﬁxed at the beginning but the discount can tory levels for individual products and bundles. More uted be adjusted); and the static price, static discount case policies recently, Gurler et al. (2005) investigate the dynamic ib (where the announced price and the discount are both pricing of two products with limited inventories,

distr ﬁxed at the beginning, and the only dynamic decision which are sold separately or as a bundle.

mission is whether an upsell offer will include the discount). and In addition, we investigate, by a numerical study, the per 2.2. Dynamic Pricing beneﬁts of using purchase information, dynamic pric- Our work is also closely related to the stream of re- ticle and ing, and dynamic discounting. ar search dealing with dynamic pricing of limited inven- In the next section, we position our work with tories pioneered by Gallego and van Ryzin (1994) ights this r respect to the existing literature. We then describe the and by Bitran and Mondschein (1997). (In particu- to model in §3 for the case where the announced price lar, our model follows the framework used by Bitran is dynamically adjusted and the discount level is cus- and Mondschein in that we divide the selling sea- tomized for each customer. Section 4 presents a dis- including son into short discrete time intervals.) For recent yright cussion of our results for that case. In §5, we consider reviews of the literature on dynamic pricing of lim- cop the static price, dynamic discount and static price, ited inventories, see Bitran and Caldentey (2003) and

mation, static discount cases. We discuss the results of our Elmaghraby and Keskinocak (2003). As dynamic pric- or numerical study in §6. We conclude with a discussion holds

inf ing has become more popular in the retail industry, of future research directions in §7. it has been receiving increased attention. Many inter- 2. Literature Review esting variations of the problem have been considered recently, such as dynamic pricing for multiple We discuss the relevant prior work under three head- INFORMS Additional products (Zhang and Cooper 2005 and Maglaras and ings: bundling, dynamic pricing, and cross-selling Meissner 2005); dynamic pricing in the presence of and upselling. strategic consumers (Elmaghraby et al. 2008, Aviv and Pazgal 2005a); and the choice of initial stock level Stremersch and Tellis (2002) discuss the legality of bundling prac- under dynamic pricing (Monahan et al. 2004). tices and claim that any kind of bundling is legal as long as the customer has the option to purchase the products separately, which In their review paper, Elmaghraby and Keskinocak is the case in this paper. (2003) note that a promising direction for future Aydin and Ziya: Pricing Promotional Products Under Upselling Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS 363

research is the possibility of using customer-speciﬁc as the regular product. Later, we extend our results to information to make customized offers in the pres- the case where there are multiple regular products. ence of inventory considerations. We consider this in In this section, we describe our model assuming the context of upselling. In our model, the use of cus- that both the announced price of the promotional tomer purchase information is rather simple in that product and the discount that comes with an upsell the ﬁrm uses only the fact that the customer has just offer can be dynamically adjusted over time. Later, in

.org/. bought a certain product with a certain price, ignoring §6, we will modify this model to analyze the cases

ms any past information it might have. The firm could where the firm has limited flexibility in adjusting the author(s). or start with some beliefs on the arrival rate of customers price and/or the discount. We assume that the regular .inf the and their reservation price distributions, and could product’s price is exogenously fixed at r. This would to nals update those beliefs on the basis of observations made certainly be true in the case of a cataloger because throughout the selling season. For an analysis of such the initial prices published in the catalog cannot be tesy sophisticated uses of learning by a firm with limited changed during the relatively short selling season of inventories, see Aviv and Pazgal (2005b). the promotional product. In addition, certain retailers http://jour cour at a (e.g., retailers following the everyday-low-price for- 2.3. Cross-Selling and Upselling le mat) may avoid frequent price changes on regular as A recent work that is closely related to ours is by products, while using dynamic pricing to clear the y

ailab Netessine et al. (2006), who refer to the practice as v inventory of a promotional product. a cop cross selling. Netessine et al. (2006) address the prob- In keeping with our focus on the use of upselling to is

, lem of what additional product to offer to a customer this liquidate excess inventories, we assume that the pro- who made a purchase, i.e., the packaging question. motional item has a fixed initial inventory that needs In contrast, we eliminate the packaging question by uted to be sold by a certain deadline, and that there are policies ib assuming that the firm has already decided what no replenishment opportunities for the promotional product to offer. This simplification allows us to

distr product. Initially, we assume that the regular prod- obtain additional insights as follows: (i) Netessine

mission uct is always available when a customer demands it; et al. (2006) assume that a customer’s reservation and we relax this assumption later to consider the limited per price for a two-product package has an exogenously availability of the regular product. ticle given distribution. In contrast, we explicitly model the and ar reservation prices of a customer for individual prod- 3.1. Reservation Prices and Consumer Population

ights ucts. We ﬁnd that whether the correlation between For each product, we assume that the customer pop- this r those reservation prices is negative or positive has a ulation is clustered into two segments: the target to substantial effect on pricing decisions. (ii) In addition segment and the nontarget segment. The target cus- to the case of static announced prices considered by tomers are the primary consumers of the product, including yright Netessine et al. (2006), we consider the case where whereas the nontarget customers are all the others in the promotional product’s announced price is dynam- the population. A customer may belong to the target cop ically adjusted. This allows us to gain insights into the segment of one product and the nontarget segment mation, interaction between upselling and dynamic pricing. of the other product. We use 1 as the index for the or holds

inf (iii) In upselling, knowing that the customer bought a target segment and 2 as the index for the nontarget

product at a certain price has informational value to segment. We let qRi, i = 1 2, denote the probability the ﬁrm when offering the promotional product. We that a customer belongs to segment i of the regular

are able to investigate the value of such information item. Similarly, qPi, i = 1 2, denotes the probability INFORMS Additional because we explicitly model the relationship between that a customer belongs to segment i of the promo-

the reservation prices for different products. tional item. Let ij , ij = 1 2, denote the probability that a customer belongs to segment j of the promo- 3. Model Description tional item given that she belongs to segment i of the 2 Initially, we assume that the firm is offering two prod- regular item. (Note that, by definition, j=1 ij = 1, i = ucts. One of these is the promotional product, the prod- 1 2.) For clarification, consider the following exam- uct the firm is upselling. We refer to the other product ple. Suppose the promotional product is a slow-selling Aydin and Ziya: Pricing Promotional Products Under Upselling 364 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

Figure 1 Let a b c d Denote the Fraction of Customers that Belong to Assumption 2(A2). FRi · , FPi · , i = 1 2, have the Groups Depicted in the Venn Diagram Below strictly increasing generalized failure rates.

Assumption 3(A3). FR1 · >fr FR2 · and FP1 · >fr

FP2 · . ab c Target Target The ﬁrst assumption is technical in nature. The sec- .org/. segment of segment of ond assumption is needed to provide some regularity

ms the regular d promotional

author(s). product or product to the revenue function, and it is satisﬁed by a vari-

.inf ety of probability distributions, including the positive- the Whole customer population valued part of the normal distribution and all Weibull to

nals Notes. Then: q = b + c, q = a + b, = b/ a + b , = c/ c + d . P 1 R1 11 21 distributions. (For a comparison of various assumptions on reservation prices used in revenue manage- tesy new album by the Rolling Stones and the regular product is a classic album of the Rolling Stones that has had ment problems, see Ziya et al. 2004.) The ordering http://jour cour stated in (A3) can be interpreted to mean that the

at steady sales over the years. Then, one would expect a 11 absolute price elasticity of demand of a target cus- le to be large. On the other hand, if the regular product as is an album by a pop star, say Britney Spears, then we tomer is less than that of a nontarget customer; i.e., y

ailab customers in the target segment are less price sensi- v would expect 11 to be smaller. See Figure 1 for a visual a cop tive. A further implication of (A3) is that, for each

is depiction of the problem parameters pertaining to the

, product, the reservation price of a customer in the this customer population. Note that for the model parameters to be consistent with each other, the parameter target segment stochastically dominates that of a customer in the nontarget segment, i.e., F x < F x , uted R1 R2

policies values need to satisfy the following ib and FP1 x < FP2 x , ∀ x. With these assumptions, correlation between the distr qPi = qR11i + qR22ii= 1 2 (1) reservation prices for the two products and val- mission ij and Let FRi · , i = 1 2, be the cumulative distribution ues are related as described in Proposition 1. (See per function (cdf) of the reservation price of segment i Appendix A in the online supplement for a proof.3) ticle and customers for the regular item. Similarly, FPi · , i = ar 1 2, is the cdf of the reservation price of segment i Proposition 1. Let X and Y denote the reservation

ights prices of a randomly chosen customer for the regular and this r customers for the promotional item. We let FRi x = 1 − F x and F x = 1 − F x . For two cdfs the promotional products, respectively. These two reser- to Ri Pi Pi 1 vation prices are negatively (positively) correlated (i.e., and 2 (with corresponding pdfs 1 and 2), if the Cov XY < > 0) if and only if + < > 1. failure rate of 1 is strictly less than that of 2, 11 22 including yright i.e., if x / x < x / x , ∀ x, then we say 1 1 2 2 Throughout the remainder of the paper, we will use

cop strictly dominates in failure rate ordering, 1 2 the following definition for ease of exposition. and we write > . (See, for example, Müller mation, 1 fr 2 Definition 1. If 11 + 22 < 1, we say that the pro- or and Stoyan 2002.) For any cdf and the corre- holds motional and the regular products are dissimilar. Oth- inf sponding pdf , generalized failure rate is defined erwise, we say that the promotional and the regular to be x x / 1 − x . Throughout the paper, we products are similar. use increasing/decreasing and positive/negative in Hence, in this paper, two products are dissimilar the weak sense, unless specifically qualified as strictly INFORMS Additional if a randomly chosen customer’s reservation prices increasing/decreasing or nonpositive/negative. We for the two products are negatively correlated. Other- make the following assumptions on the reservation wise, the two products are similar. price distributions. Assumption 1(A1). F · , F · , i = 1 2, are twice Ri Pi 3 An online supplement to this paper is available on the Manufac- continuously differentiable, strictly increasing functions, turing & Service Operations Management website (http://msom.pubs. and they all have the same nonnegative support. informs.org/ecompanion.html). Aydin and Ziya: Pricing Promotional Products Under Upselling Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS 365

3.2. Timing of Events the promotional item. Let dt denote the absolute dis- We now focus on the time horizon during which the count offered to the customer in the upsell stage of promotional item will be sold. We assume that each period t. Note that the ﬁrm may choose to offer no arriving customer has only one product in her consid- discount; i.e., the ﬁrm may offer the promotional item

eration set, either the regular product or the promo- at price pt. tional product.4 Henceforth, we refer to a customer as 2. The customer will purchase the promotional .org/. a potential customer for the regular product if the cus- item on the upsell offer if pt − dt is less than or equal

ms to her reservation price for the promotional item.

author(s). tomer has the regular product in her consideration or set. Likewise, a potential customer for the promotional .inf

the 3.3. Firm’s Revenue-Maximization Problem product is a customer who has the promotional prod- In the initial stage of period t, given that a potential to nals uct in her consideration set. We assume that the time customer for the regular item arrived, let r denote horizon is divided into T periods, each of which is R

tesy the probability that the customer will buy the regular short enough that either one customer arrives in each item. Note that the customer belongs to the target seg- http://jour cour period or none at all. (This assumption is common ment with probability qR1 and the nontarget segment at a in dynamic pricing models. See, for example, Bitran with probability q , and will buy the regular product

le R2 as and Mondschein 1997.) If an arriving consumer is a with probability FR1 r if she is in the target segment y potential customer for the regular product and ends ailab and with probability F r if she is in the nontarget

v R2 a cop up buying it, then the ﬁrm offers her the promotional segment. Therefore, we can write R r as follows is product. To model this process, we divide each period ,

this into two stages: initial stage and upsell stage. In the R r = qR1FR1 r + qR2FR2 r initial stage, the following is the sequence of events. Henceforth, we write r as , because the regu- uted R R policies ib 1. At the beginning of the initial stage, the seller lar product’s price, r, is exogenous to our model. Let announces pt, the price for the promotional item that P pt denote the probability that a customer will buy distr will be in effect during the initial stage of period t. the promotional item, given that a potential customer mission (Recall that the regular item’s price is ﬁxed at r.) and for the promotional item arrived in the initial stage of per 2. During the initial stage, one of three events hap- period t to observe the announced price of pt. Then

ticle pens: A potential customer for the regular item arrives and we can write P pt as follows ar with probability ; a potential customer for the pro- R P pt = qP1FP1 pt + qP2FP2 pt (2) ights motional item arrives with probability P ; and no cus- this r tomer arrives with probability 1 − R − P . If a customer buys the regular product, this pro- to 3. A potential customer for the regular product will vides the ﬁrm with additional information about purchase it if r is less than or equal to her reserva- the customer, namely, that the customer’s reservation including yright tion price for the regular item. Likewise, a potential price for the regular product is above r. When making customer for the promotional product will purchase an upsell offer, the ﬁrm can use this new information cop

it if pt is less than or equal to her reservation price for to update the probabilities with which the customer mation,

or the promotional item. belongs to the target and nontarget segments of the holds inf The upsell stage occurs only if a customer arriving promotional item. Let qˆP1 denote the probability that a in the initial stage purchases the regular item. The customer belongs to the target segment of the promo- following is the sequence of events for the upsell stage tional item given that she purchased the regular item

in a period. in the initial stage, and qˆP2 the probability that she INFORMS Additional 1. The customer who purchases the regular item in belongs to the nontarget segment. Using Bayes’ rule, the initial stage receives an offer from the ﬁrm for we can write these updated probabilities as follows q F r + q F r ˆ R1 11 R1 R2 21 R2 4 A consideration set is the set of products the consumer is con- qP1 = R sidering for purchase. It would not be too difﬁcult to extend the (3) model to allow a third class of customers who have both products q F r + q F r qˆ = R1 12 R1 R2 22 R2 in their consideration set. P2 R Aydin and Ziya: Pricing Promotional Products Under Upselling 366 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

Let x denote the probability that a customer will period t − 1 when there are y units in inventory, i.e., buy the promotional item on an upsell offer when the the marginal value of one unit of inventory. Define firm offers her the promotional product at a price of x. #1 p" = P p p − " (6) If the firm offers a discount dt from the announced price p , the customer will be facing a price of p − d t t t #2 p" = p p − " (7) for the promotional product. The following gives the .org/. probability that such a customer will buy the promo- Here, #1 p" can be interpreted as the expected ms tional item marginal contribution from one unit of the promo- author(s). or tional item in the initial stage of a period when

.inf the pt − dt = qˆP1FP1 pt − dt + qˆP2FP2 pt − dt (4) the announced price is set at p and the marginal to nals value of one unit of the promotional item is ". Like- Now we are ready to formulate the dynamic pro- wise, # p" is the expected marginal contribution gram for the ﬁrm’s revenue-maximization problem 2 tesy from one unit of the promotional item in the upsell over the T -period horizon. (We will denote the ﬁrst

http://jour stage, when the upsell price is p. Given # p" and cour period as period T and the last period as period 1.) 1 at a #2 p" as defined by (6) and (7) and the optimality Let Vt y denote the firm’s optimal expected revenue le equations in (5), the maximization problem the firm as from the promotional product when starting period t

y is solving for a given t and y can be written as

ailab with y units of inventory. The optimality equations v

a cop are given by max # p " yt

is P 1 t p d p ≥d ≥0 , t t t t this V y = max p −d p −d +V y−1 ! t R R t t t t t−1 + # p − d " yt (8) pt dt pt ≥dt ≥0 R R 2 t t uted

policies + P P pt pt + Vt−1 y − 1 ib Deﬁne

+ 1 − RR pt − dt

distr ∗ ∗ ∗ z1 yt = inf p #1 p " yt

mission − P P pt Vt−1 y and ≥ #1 p" yt ∀ p % (9) per y>0t= 1 T ∗ ∗ ∗ z2 yt = inf p #2 p " yt ticle and V 0 = 0t= 1 T and V · = 0

ar t 0 ≥ #2 p" yt ∀ p % (10)

ights The ﬁrst term of V y is the revenue-to-go in the this r t event that a customer purchases the promotional z∗ yt =inf p∗ # p∗" yt + # p∗" yt to P 1 R R 2 product on an upsell offer, the second term is the ≥ P #1 p" yt revenue-to-go if a customer arrives to purchase the including yright promotional product in the ﬁrst place, and the third +RR#2 p" yt ∀ p (11) term is the revenue-to-go if no promotional product cop is sold in that period. The terminal conditions indi- In light of the interpretations of #1 p" and #2 p" mation, discussed earlier, we can interpret z∗ yt and z∗ yt

or cate that the salvage value of the item is zero, an 1 2 holds inf assumption that could be relaxed. After some alge- as follows. With y units in inventory and t periods ∗ to go, z1 yt is the announced price that maximizes braic manipulation, one can write Vt y as follows the proﬁt in the initial stage of period t and z∗ yt 2 Vt y = Vt−1 y + max P P pt pt − " y t is the upsell price that maximizes the proﬁt in the p d p ≥d ≥0

INFORMS Additional t t t t upsell stage of period t. Likewise, z∗ yt would be + RR pt − dt pt − dt − " y t the price the ﬁrm would choose if it had to use the

y>0t= 1 T (5) same price in both stages. (When #i p" has mul- ∗ ∗ tiple optima, zi yt and z yt are taken to be the where " y t = Vt−1 y − Vt−1 y − 1 . Here, " y t smallest maximizers.) It is easy to construct numerical can be interpreted as the expected future beneﬁt examples to demonstrate that #1 p" and #2 p" from carrying one unit of the promotional item into are not necessarily unimodal in p. Nevertheless, the Aydin and Ziya: Pricing Promotional Products Under Upselling Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS 367

possibly complicated behavior of these functions does Given the result of Proposition 2, intuition would not render the problem intractable insofar as one can suggest that if the two products are dissimilar, then obtain a number of results on the optimal announced a customer who bought the regular product should price and discount levels, which we discuss next. be given a discount on the promotional item as part of the upsell offer (because a customer who bought the regular item, compared to a random customer, is

.org/. 4. Dynamic Prices and Discounts less likely to be in the target segment of the promo-

ms Here, we ﬁrst discuss our analytical results for the tional item and, hence, more likely to have a smaller author(s). or base model presented in the previous section. We then reservation price for the promotional item). On the .inf

the discuss how these results change with changes in the other hand, if the two products are similar, then a cus- to nals model (under limited availability of the regular prod- tomer who bought the regular item is more likely to uct and when there are multiple regular products). be in the target segment of the promotional item, so tesy the firm will not offer a discount from the announced 4.1. Results for the Base Model http://jour cour price. If anything, the firm would like to charge an One question of interest is whether the firm should at a upsell price in excess of the announced price (had it accompany upsell offers with discounts on the pro- le

as been allowed), because a customer buying the regu- motional item and, if so, how deep those discounts y lar product signals a higher willingness to pay for the ailab

v should be. The answer to this question is closely

a promotional product as well. Theorem 1 formalizes cop related to the following comparison. Consider a cus- is this result. , tomer randomly drawn from the population and this ∗ ∗ ∗ another customer who is known to have purchased Theorem 1. Let z1 yt , z2 yt , and z yt be as defined by (9), (10), and (11). Given y units in inventory uted the regular item. Which customer is more likely to policies ib be in the target segment of the promotional item? and t periods to go (a) If the two products are dissimilar, then the firm offers distr In other words, using the notation defined earlier, a discounted upsell price. In particular, we have z∗ yt > mission which probability is larger: qP1 or qˆP1? As the follow- 1 ∗ ∗ and ing proposition states, this comparison is decided sim- z2 yt , and it is optimal for the firm to set pt = z1 yt per and d = z∗ yt − z∗ yt > 0. ply on the basis of the values of ij s. (The proofs of t 1 2 ticle and all the results in this section are given in Appendix A (b) If the two products are similar, then the firm does ar of the online supplement.) not offer a discount as part of the upsell offer. In particular,

ights ∗ ∗ ∗ this r we have z1 yt ≤ z yt ≤ z2 yt , and it is optimal to Proposition 2. In comparison to a random customer, ∗ to set pt = z yt and dt = 0. a customer who is known to have bought the regular item Hereafter, we let p∗ y and d∗ y denote the opti- is less likely to be in the target segment of the promotional t t

including mal price and discount pair prescribed by Theorem 1, yright item if and only if the regular and the promotional items are dissimilar, i.e., qˆ

larger 22 is, the more likely it is that a nontarget cus- the ﬁrm sacriﬁces some of its initial-stage revenues tomer for the regular item is also a nontarget cus- but improves its upsell-stage revenues by charging an

INFORMS Additional tomer for the promotional item. Proposition 2 states ∗ upsell price in excess of z1 yt . When the two prod- that if 11 + 22 < 1 (with the minimum possible sum ucts are dissimilar, no such trade-off occurs, because being zero and the maximum possible sum being the ﬁrm would prefer charging an upsell price lower two), then a customer who bought the regular prod- than the announced price. uct is less likely to be a target customer for the promo- One important implication of Theorem 1 is that tional product, compared to a customer chosen from whether the ﬁrm will offer a discount has nothing to the population at random. do with time or inventory, but depends entirely on Aydin and Ziya: Pricing Promotional Products Under Upselling 368 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

the similarity of the products (i.e., correlation between The proposition states that both the optimal the reservation prices for the two products). However, announced price and the optimal upsell price will be in cases where the ﬁrm chooses to offer a discount, lower if there is more inventory of the promotional ∗ ∗ ∗ the size of the discount, dt y = z1 yt −z2 yt , does item or if there is less time until the end of the hori- depend on t and y. zon. However, the difference between the two, the

Next, we state a result that characterizes how Vt y optimal discount, turns out to be nonmonotonic in .org/. and " y t = Vt−1 y − Vt−1 y − 1 depend on t and y. time at a ﬁxed inventory level and in inventory level ms This result is important in that it helps us understand

author(s). at a ﬁxed time, as shown in Figure 2. As inventory or how the optimal announced prices and upsell prices level increases, the discount may increase ﬁrst, but .inf the depend on time and inventory level. once the inventory level becomes large enough, the to nals Proposition 3. Given y ≥ 1 units in inventory and announced price starts dropping so fast that the dis- t ≥ 1 periods to go, we have count needed to get to the optimal upsell price starts tesy (a) " y t + 1 ≥ " y t , to decrease. In addition, there are examples showing http://jour cour (b) " y t ≥ " y + 1t , that not only the nominal discount, but also the per- at a centage discount, is not monotone with respect to the (c) Vt+1 y − Vt y ≥ Vt+2 y − Vt+1 y . le

as inventory level and time. The ﬁrst part of the proposition states that the y ailab v marginal value of one unit of the promotional item 4.2. Limited Availability of the Regular Product a cop is decreasing as we are getting closer to the end of is Our original model introduced in §3 assumes that the , this the horizon. The second part implies that the same regular product is always available when demanded. marginal value is larger when there are fewer items However, if the regular product is a fast-selling

uted in inventory. Finally, part (c) of the proposition says policies seasonal product, then there is a chance that it might ib that, at a ﬁxed y, the revenue-to-go function is convex go out of stock, which would in turn affect the pricing distr in t. Given the results of Proposition 3, the following decisions for the promotional product. If it is proﬁtable

mission results that characterize the behavior of the optimal for the ﬁrm to make emergency replenishments when- and announced price and the optimal upsell price in t per ever the regular product is demanded but is out of and y are to be expected. stock, then the promotional product would be offered ticle and ar Proposition 4. Both the optimal announced price to the customer regardless of the on-hand inventory (i.e., p∗ y ) and the optimal upsell price (i.e., p∗ y − level of the regular product. As a result, the limited ights t t this r ∗ dt y ) are decreasing in inventory (y) and increasing in availability of the regular product would not have any to time-to-go (t). effect on the pricing of the promotional product and all including yright Figure 2 Discount Is Not Monotonic in Time-to-Go at a Fixed Inventory Level and in Inventory Level at a Fixed Time-to-Go

cop Discounts when y = 2 Discounts when t = 10 14 14 mation,

or 12 12 ) ) holds inf ( y * ( y * 10 t 10 t

8 8

6 6 INFORMS Additional 4 4 Discount level d Discount level d 2 2

0 0 1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 171819 20 1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 171819 20 Time (t) Inventory level (y)

Notes. In this example, 11 = 0, 22 = 0, qR1 = 0 3, P = 0 2, R = 0 5, r = 65 and FP 1, FP 2, FR1, FR2 are all Weibull distributions with shape and scale parameters given by, respectively, 2 90 , 2 50 , 2 100 , and 2 50 . Aydin and Ziya: Pricing Promotional Products Under Upselling Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS 369

of our results for the unlimited availability case would Proposition 5. Suppose that the regular product and go through. (For more on the use of emergency replen- the promotional product are dissimilar. Then, for x ≥ 0, ishment in a similar context, see Netessine et al. 2006.) y ≥ 0, t ≥ 1, we have Here, we investigate how the pricing and discounting (a) " x + 1y+ 1t ≥ " x y + 1t , decisions are affected if the emergency replenishment (b) " x y + 2t ≤ " x y + 1t , option is not available to the ﬁrm. (c) " x y + 1t+ 1 ≥ " x y + 1t . .org/. Let Vt xy denote the ﬁrm’s optimal expected rev-

ms Parts (b) and (c) of Proposition 5 extend Proposi-

author(s). enue from the promotional product when starting or period t with x units of the regular product and tion 3 to the case where the regular product has lim- .inf the y units of the promotional product. Then, the opti- ited availability. In addition, Proposition 5(a) states to nals mality equations are given by that the marginal value of one unit of the promotional product increases with the inventory level of the reg- tesy ular product. This result is not surprising because Vt xy

http://jour higher inventory levels of the regular product imply cour = max RR pt −dt pt −dt +Vt−1 x−1y−1 at a pt dt pt ≥dt ≥0 more opportunities for upselling (and thus selling

le the promotional product) until the end of the season. as + 1 − pt − dt Vt−1 x − 1 y !

y From Proposition 5(a), it follows that compared with ailab v + P P pt pt + Vt−1 xy − 1 the case where the regular product is always avail- a cop

is + 1 − p V xy ! able when demanded, in the limited availability case, , P t t−1 this the marginal value of the promotional product will + 1 − − V xy R R P t−1 be smaller. Therefore, it is reasonable to expect that uted policies x>0y>0t= 1 T one would be more inclined to offer discounts. Using ib Proposition 5(a), we can prove the following theorem: distr Vt 0y = max P P pt pt + Vt−1 0y− 1 pt pt ≥0 mission Theorem 2. Suppose that there is a ﬁnite amount of and the regular product at time T and its inventory is never per + 1−P pt Vt−1 0y !+ 1−P Vt−1 0y replenished. Furthermore, suppose that the regular and pro- ticle y>0t= 1 T and motional products are dissimilar. Then, the ﬁrm offers a ar

Vt x0 =0x≥0t=1 T and V0 · =0 (12) discounted upsell price. ights this r Theorem 2 states that the ﬁrm always offers dis- to For any given state with t>0, x>0, and y>0, the single-period optimization problem can be written as counts when the regular and promotional products are dissimilar. For such products, the following

including yright max RR pt − dt pt − dt − " x − 1yt proposition further describes how the announced pt ≥dt ≥0 cop price and the upsell price depend on the inventory + p p − " x y t (13)

mation, P P t t levels of the regular and promotional products and

or time until the end of the season. holds

inf where Proposition 6. Suppose the regular and promotional

" x y t = Vt−1 xy − Vt−1 xy − 1 products are dissimilar. Then, both the optimal announced price and the optimal upsell price are decreasing in inven- INFORMS Additional Note that " x y t can be interpreted as the marginal tory of the promotional product (y), increasing in the value of one unit of the promotional product in inventory of the regular product (x), and increasing in period t when there are x units of the regular product time-to-go (t). and y units of the promotional product. The following proposition describes how " x y t changes with Theorem 2 and Proposition 6 concern products that x, y, and t. (See Appendix B in the online supplement are dissimilar. As for similar products, recall from for the proofs of the results in this section.) Theorem 1 that when the regular product is always Aydin and Ziya: Pricing Promotional Products Under Upselling 370 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

available, customers are never offered discounts. In results of the dynamic price, dynamic discount model contrast, when the regular product has limited avail- to this case. A detailed development of the model ability, the ﬁrm may choose to offer discounts. Con- along with the additional notation needed, is given in

sider the example where qR1 = 0 7, qP1 = 0 7, 11 = Appendix C in the online supplement. Here, we will 22 = 1, R = 0 25, P = 0 25, r = 85, FR1, FR2, FP1, provide only the notation needed to summarize the and FP2 are all Weibull distributions with shape and results. With n regular products, in each period, one .org/. scale parameters 2 100 , 2 50 , 3 190 , and 3 150 , of n + 2 events happens in the initial stage: A poten-

ms respectively. For this example, when there is one unit tial customer for regular product k ∈ (1 n) may author(s). or of promotional product and one unit of regular prod- arrive, or a potential customer for the promotional .inf the uct in inventory, and there are 12 time periods left, the product may arrive, or no customer arrives at all. In to nals ﬁrm will offer a discount of approximately 6.3 from the upsell stage, when making an upsell offer to a cus- the announced price. tomer who bought one of the regular items, the ﬁrm tesy When the two products are similar, one might can offer different discounts to different customers

http://jour expect certain monotonicity structures on discount- based on which regular product the customer bought. cour at a ing decisions to hold. For example, one would expect Let qˆPik denote the probability that a customer

le Proposition 6 to hold even when the two products belongs to segment i of the promotional item (seg- as

y are similar, and indeed our numerical study supports ment 1 being the target segment, and segment 2 the ailab

v that claim. On the other hand, however, certain mono- nontarget), given that the customer bought regular a cop

is tonicity properties that might be expected to be true product kk = 1 n, in the initial stage of a period. , this do not hold. For example, in some cases, although dis- In the rest of this section, it will be convenient to count is being offered at a certain inventory level (of assume that the regular items are indexed in ascend- uted

policies the regular or promotional product), it is not offered ing order of qˆP1ks; i.e., they are indexed so that qˆP11 ≤ ib at higher and lower levels of inventory, indicating that qˆP12 ≤ ··· ≤ qˆP1n. Then a customer who bought reg- distr optimal discount policy does not have a simple mono- ular item i in the initial stage is less likely to be

mission tonic structure with respect to inventory levels. (See in the target segment of the promotional item, com- and

per Figure 3 for an example.) pared to customers who bought regular items i + 1or higher. Given this indexing of the regular products, ticle and 4.3. Multiple Regular Products one would expect the ﬁrm to be more willing to offer ar In §4.1, we derived all our results for the case where a discount to purchasers of lower-indexed regular ights this r there is one product in addition to the promotional items compared to purchasers of higher-indexed reg- to one. Suppose now that there are n ≥ 2 regular prod- ular items. The next theorem states this result, among ucts instead of just one. In this section, we extend the others. (See Appendix C in the online supplement for

including a proof.) yright Figure 3 Optimal Discount Policy for t = 20 Theorem 3. Suppose the regular products are indexed cop Optimal discount policy so that qˆP11 ≤ qˆP12 ≤···≤qˆP1n. Given y units of the pro- mation, ) motional item in stock and t periods to go, let p and d or 7 t tk holds

inf denote, respectively, the announced price of the promotional Do not offer discount item in period t and the discount offered on the promo- 5 tional item to a customer who purchased regular item k in the initial stage of period t. Then 3 INFORMS Additional Offer discount (a) If regular product k ∈ (1 n) is dissimilar to the promotional one, i.e., + < 1, then the ﬁrm offers a 1 11k 22k Inv. of the reg. product ( x nonzero discount when making upsell offers to customers 13 5 79 111315 who buy regular product k; i.e., it is optimal for the ﬁrm Inv. of the prom. product (y) to set d > 0. Notes. In this example, = 0 3, = 1, q = 0 7, = 0 25, = 0 5, tk 11 22 R1 P R (b) Suppose there exists at least one regular product r = 85 and FP 1, FP 2, FR1, FR2 are all Weibull distributions with shape and scale parameters given by, respectively, 3 90 , 3 150 , 2 100 , and 2 50 . that is dissimilar to the promotional product. Then, there Aydin and Ziya: Pricing Promotional Products Under Upselling Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS 371

exists m ∈ (1 n) such that the ﬁrm offers a nonzero 5.1. Static Price and Dynamic Discounts discount when making upsell offers to customers who buy First, consider the case where the ﬁrm charges

regular product k for k ≤ m; i.e., it is optimal to set dtk > 0 announced price p over the entire horizon, but is free for k ≤ m. Furthermore, for any two products i

ms of time and inventory, purchasers of any regular item can show a result analogous to Propositions 3 and 5. author(s). or that is dissimilar to the promotional item will receive The marginal value of one unit of the promotional .inf the discounted upsell offers. This is similar to the result product increases in the remaining time (t) and inven- to nals in the case of a single regular product. In addition, as tory level of the regular product (x) and decreases in stated in part (b), all customers who purchased regu- the inventory level of the promotional product (y). tesy lar items 1 through m will receive discounted upsell Given such a result on the marginal value, one can http://jour cour offers for some m ∈ (1 k). What is implicit in the establish the following proposition, which states the at a statement of part (b) is that some of these m prod- effects of inventory levels and remaining time on the le as ucts may be similar to the promotional product, but decision to offer a discount. y

ailab customers who purchase these regular products will Proposition 7. Suppose the announced price is ﬁxed v a cop nevertheless receive discounted upsell offers. This is at some p. is

, in contrast to the single regular product case, where (a) At any ﬁxed inventory levels y for the promotional this a customer never receives a discount if the regular product and x for the regular product, if it is optimal to product is similar to the promotional product. Here is pick some d > 0 at any time t = t , then it is also optimal uted t 0 policies ib the intuition behind this result. Among all the regular to pick some dt > 0 for any t 0

mission t and tional item, i.e., products for which qˆP1k is particularly when there are y = y0 units in inventory, then it is also per large. Purchasers of such regular products are willing optimal to pick some dt > 0 when there are y>y0 units in ticle and to pay relatively high prices for the promotional item. inventory. ar In order to be able to charge high upsell prices to (c) At any fixed time t and fixed inventory level y for ights this r such customers, the firm keeps the announced price the promotional product, if it is optimal to pick some dt > 0

to high, and offers a discount to purchasers of regular when there are x = x0 units in inventory, then it is also optimal to pick some d > 0 when there are x

including though those products may be similar to the promo- yright tional one. According to Proposition 7, when price is static, the cop discount policy is the switching-curve type, as shown mation, in Figure 4. (For purposes of this ﬁgure, we assumed or holds 5. Static Price and/or Discount

inf that the regular product is always available when So far we have assumed that the ﬁrm can adjust both demanded; i.e., x is larger than the number of periods the announced price and the discounts dynamically. to go, 20.) In addition, we note that even when the In this section, we consider the ﬁrm’s revenue- regular product is always available and the two prod-

INFORMS Additional maximization problem when the firm has less flexibil- ucts are similar, it is possible that the firm will offer ity in adjusting the announced price and the discount.5 a discount along with the upsell offer, which would never happen in the case in which the announced price is set dynamically. 5 Here, we provide only an overview of the results for the case of The pricing problem that arises in this case is akin static price and/or discounts. A more detailed version of this section and formal proofs of the results are available from the authors to that considered by Netessine et al. (2006), who fix upon request. the prices of the products, but allow the price of a Aydin and Ziya: Pricing Promotional Products Under Upselling 372 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

Figure 4 When the Announced Price Is Fixed at the Beginning, There discount. This ordering depends on qˆP1k, k = 1 n, Is a Boundary of Inventory Level and Time-to-Go Pairs Above the probability that a customer who bought regular Which It Is Optimal to Offer a Discount product k in the initial stage belongs to the target seg- Optimal discount policy ment of the promotional product. For any two regu- 8 lar products i and j, the fact that qˆP1j ≥ qˆP1i indicates 7 Offer discount that purchasers of product j are willing to pay more

.org/. 6

) than the purchasers of product i for the promotional

ms 5 product. Therefore, for any ﬁxed inventory levels and author(s). or 4 time, customers who purchase product j are going to .inf the 3 get a discount only if the purchasers of product i get Inventory ( y to nals 2 Do not offer discount a discount. 1 tesy 0 6. Numerical Study 1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 171819 20 http://jour cour Time-to-go (t) So far, we have considered three different types of at a pricing and discounting policies: dynamic pricing and Notes. In this example, T = 20, 11 = 0, 22 = 0, qR1 = 0 3, P = 0 2, R = le as 0 5, r = 65 and FP 1, FP 2, FR1, FR2 are all Weibull distributions with shape and dynamic discounting policy (DPDD), static pricing y scale parameters given by, respectively, 2 90 , 2 50 , 2 100 , and 2 50 . and dynamic discounting policy (SPDD), and static ailab v a cop pricing and static discounting policy (SPSD). In a

is two-product bundle to be determined optimally every DPDD policy, all decisions related to the promo- , this time a consumer is offered a bundle. In fact, we follow tional product are dynamic. Prices are set dynami- their approach in establishing some of our results. cally, the decision of whether to offer a discount is uted policies made dynamically, and the level of the discount is ib 5.2. Static Price and Discount determined dynamically depending on the inventory distr Here, both the announced price, p, and the discount level and time. In an SPDD policy, the advertised

mission level, d, are ﬁxed at the beginning of the horizon. price of the product is kept the same throughout and

per In this case, the only dynamic decision available to the time horizon, whereas discount decisions are still the firm is whether to offer the discount in a given ticle dynamic. Finally, in an SPSD policy, the only dynamic and ar period with given inventory levels. As in the static decision is whether to offer a discount to a customer, price-dynamic discount case, it can be shown that the whereas the advertised price and the discount that ights this r optimal discount policy is of switching-curve type. will be offered are fixed throughout the season. We to In addition, it is easy to show that for a fixed initial note that under the SPSD policy, the static price and price p, at any given time t and inventory levels x discount are chosen optimally at the beginning of the including

yright and y, if it is optimal to offer a discount in the static horizon. Likewise, under the SPDD policy the static discount model, it is also optimal to offer a discount price is chosen optimally. cop in the dynamic discount model. This is not surprising, We generated 24,300 different problem instances, mation, because one would be more inclined to offer discounts and for each instance we identiﬁed the optimal or holds

inf when there is the ﬂexibility of choosing the discount prices and discounts over a 20-period horizon under level depending on the system state. each pricing-discounting strategy (DPDD, SPDD, and SPSD). Finding the optimal solution for each problem 5.3. Multiple Regular Products instance requires solving a dynamic program to opti-

INFORMS Additional Proposition 7 can be generalized to the case where mality, each of which takes a negligible amount of there are n>1 regular products. In addition, regard- time. Initially, we identiﬁed several key model param- less of whether discounts are dynamic or static, one eters and determined a value set for each parame- can establish a result that orders the n regular prod- ter. (Parameters were assigned one of the values from ucts such that the purchaser of a lower-ranked regular this set.) Then, instances were generated by consid- product will be offered a discount only if the pur- ering all possible combinations within these sets and chaser of a higher-ranked regular product is offered a among the parameters. Table 1 lists these parameters Aydin and Ziya: Pricing Promotional Products Under Upselling Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS 373

Table 1 Parameter Value Sets inventory level of the promotional product. The optimality equations will be given by Parameter Value set q 0 3 0 5 0 7 R1 Vt y = max RR P pt pt + Vt−1 y − 1 ! p p ≥0 11 0 0 0 3 0 5 0 7 1 0 t t 0 0 0 3 0 5 0 7 1 0 22 + p p + V y − 1 + 0 3 0 5 0 7 P P t t t−1 R P .org/. R/ R + P 0 3 0 5 0 7 + 1 − RRP pt − P P pt Vt−1 y

ms rlow medium high author(s). or Initial inventory low medium high y>0t= 1 T WR1WR2 100 50 80 70 .inf the W W 90 50 75 65 P 1 P 2 Vt 0 = 0t= 1 T and V0 · = 0

to T20 nals Likewise, one could write the optimality equations for tesy and their value sets. We assumed Weibull distribu- the SPDD and SPSD policies when purchase information is not used. Of course, regardless of the pricing http://jour cour tion for FR1, FR2, FP1, and FP2. In Table 1, WR1 and at a and discounting strategy, the use of purchase infor- WR2 denote the Weibull scale parameter for FR1 and

le mation will never worsen the ﬁrm’s expected proﬁt. as FR2, respectively. (The shape parameters are two for y both.) Similarly, W and W denote the Weibull scale Here, we investigate whether the improvement due to

ailab P1 P2 v purchase information differs signiﬁcantly across pric- a cop parameter for FP1 and FP2. (The shape parameters are

is three for both.) The “low,” “medium,” and “high” val- ing and discounting strategies. Table 2 gives percent- , this ues for r and the initial inventory are not predeter- age improvements in proﬁts under DPDD, SPDD, and mined. For r, low corresponds to the value of the scale SPSD policies. uted policies parameter of the reservation price distribution for the Numbers suggest that, overall, improvements ib nontarget segment, high corresponds to the value of under the SPDD policy are signiﬁcantly larger than distr the scale parameter of the reservation price distribu- the improvements under the DPDD and SPSD poli-

mission tion for the target segment, whereas medium corre- cies. Under any pricing/discounting policy, the use and

per sponds to the weighted average of the two values of purchase information improves the ﬁrm’s revenues by helping the ﬁrm make better discounting deci- ticle with respect to segment probabilities, q and q . For

and R1 R2 ar the initial inventory level, we first calculate an upper sions. By using the DPDD policy, the firm is already bound on the total demand over the whole horizon by capturing large revenues due to the flexibility of ights this r ¯ I = R + P T . The low inventory level corresponds to ¯ ¯ to 0 2 I, the “medium” level corresponds to 0 5 I, Table 2 Improvements in Profits when Using Customer and the high level corresponds to 0 8 I¯. Purchase Information including yright Percent of improvement DPDD SPSD SPDD 6.1. Benefits of Using Customer cop Purchase Information 9 10 001

mation, We ﬁrst investigate the improvements in proﬁts 8 9 001

or 7 8 002 holds

inf brought by using the customer purchase information 6 7 004 while making upsell offers. Firms may simply choose 5 6 005 not to use this information or they may not know how 4 5 10 6 23 3 4 5771 to use it. (If the ﬁrm does not know ij values, which 2 3 41 40 314

INFORMS Additional relate the two products, then the purchase informa- 1 2 154 144 2401 tion is useless.) In such a case, there is no informa- 0 1 24090 24103 21479 tion that would distinguish the purchaser of a regular Average 0.047 0.049 0.404 Min 0.000 0.000 0.000 product from a random customer. Hence, in the case Max 4.556 4.506 9.639 of DPDD policy, there is also no need to change the Notes. Numbers represent the number of instances, DPDD: dynamic price for the upsell offer because the announced price price, dynamic discount, SPSD: static price, static discount, SPDD: has already been adjusted according to time and the static price, dynamic discount. Aydin and Ziya: Pricing Promotional Products Under Upselling 374 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

adjusting the price, hence the use of purchase infor- Table 3 Percentage Improvements in Profits Obtained by Switching mation leads to only modest improvements. Likewise, from Less Sophisticated Policies to More Sophisticated Policies when the firm is using the SPSD policy, the improvement due to the use of purchase information is small FS FS FS SPSD SPSD SPDD vs. vs. vs. vs. vs. vs. because the firm’s flexibility is limited to deciding SPSD SPDD DPDD SPDD DPDD DPDD whether to offer the discount, which limits the firm’s .org/. ability to exploit purchase information to make bet- Max 3.0447 3.8301 7.1513 1.0830 6.5409 6.5038 Min 0.0000 0.0000 0.0001 0.0000 0.0001 0.0001 ms ter discounting decisions. However, when the firm author(s). Average 0.2905 0.3489 1.9607 0.0579 1.6624 1.6030 or is using the SPDD policy, setting the right discount .inf the level is more important because dynamic discounts be obtained by switching from less sophisticated to nals can partially capture revenue management benefits policies to more sophisticated ones and determined that are not realized due to the static price. Hence,

tesy the average, maximum, and minimum improvements the use of purchase information leads to the high- over the 24,300 instances. The results are given in http://jour cour est improvements under this policy. This observation Table 3. at a suggests that firms who do not have the flexibility Table 3 clearly demonstrates the benefits of using le

as to change prices dynamically but can adjust the dis- dynamic policies—in particular, the fully dynamic y count levels (e.g., catalog retailers) will ﬁnd using the ailab policy DPDD over the fully static FS with an average v a cop customer purchase information more valuable. improvement close to 2%. From the table, one can is

, make the following observations. this 6.2. Beneﬁts of Dynamic Pricing and Discounting Decisions 6.2.1. Dynamic Pricing vs. Dynamic Discounting. uted

policies Despite the clear advantage of dynamic policies, they The average revenue improvement that would be ib are not always preferred, for various reasons. Some obtained by switching from SPDD to DPDD is around distr ﬁrms simply do not want to upset their customers 1.6%, whereas the average improvement that would

mission by changing prices frequently, whereas some oth- be obtained by switching from FS to SPDD is around and

per ers do not have the technical capabilities required 0.35%. Therefore, although dynamic discounting deci- for the implementation of such policies. Therefore, sions bring modest improvements, setting the price ticle and dynamically seems to have a much more significant ar it is of interest to understand the potential benefits that would be gained through dynamic pricing effect. ights this r and discounting decisions. Here, we report our find- 6.2.2. Dynamically Changing Discount Levels vs. to ings based on our numerical study. The pricing and Dynamically Deciding to Offer a Fixed Discount. discounting policies we consider can be ordered as Consider a firm currently using the FS policy. Fur-

including DPDD, SPDD, and SPSD from more sophisticated to yright thermore, suppose this firm is committed to using a less sophisticated. However, some firms may not even static announced price; for example, the firm may be cop have the means to implement SPSD policies. They a catalog retailer. There are two improvements such mation, may determine a discount level for the product (as a firm can make: switching to SPSD policy or the or holds

inf in an SPSD policy) and offer this discount to all the SPDD policy. We observe from the table that switch- purchasers of the regular products (unlike in an SPSD ing from the FS policy to SPDD leads to an average policy, where the ﬁrm decides optimally whether to revenue improvement of 0.35%, whereas switching offer the discount.) We call this a Full Static (FS) pol- from the FS policy to SPSD leads to an average rev-

INFORMS Additional icy. In an FS policy, there is no dynamic decision at enue improvement of 0.29%. Therefore, most of the all, but as in the SPSD policy, the static price and the revenue improvement a firm can realize by switch- discount level are determined optimally at the begin- ing to SPDD can be realized by switching to SPSD. ning of the horizon. Hence, our numerical analysis suggests that the firms For the 24,300 different instances generated, we would reasonably benefit from having the capability computed the profits under each policy. We then, of deciding when it is best to offer a discount, but computed the percentage improvements that would given that capability, having the additional flexibility Aydin and Ziya: Pricing Promotional Products Under Upselling Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS 375

of changing the discount level is beneficial to a lesser important to have a model in which the parameters degree. can be reliably estimated. Our consumer model may prove to be advantageous in this regard, because it 7. Conclusion does not require estimation of joint distributions for In this paper, we investigated the interactions among reservation prices of multiple products. Instead, the upselling, the use of customer purchase information, correlation across products is captured through cross- .org/. and dynamic pricing. We found that if the price of the segment probabilities (e.g., the probability that a cus- ms tomer who belongs to the target segment of a product author(s). promotional product is dynamically adjusted and the or regular product is always available when demanded, belongs to the target segment of the other product .inf the all customers who buy a regular product that is dis- as well). Such cross-segment probabilities can be esti- to nals similar to the promotional one (i.e., a product whose mated while conducting the initial market segmen- reservation price is negatively correlated with that of tation. For example, conjoint analysis is widely used tesy the promotional product) will be offered a discount for market segmentation, and there is a large body of http://jour cour along with the upsell offer, regardless of the inventory research on this. (See, for example, Green and Krieger at a of the promotional product and the time until the end 1991 for an overview of using conjoint analysis for le as of the selling season. However, if the firm uses a fixed segmentation, and Vriens et al. 1996 for a comparison y price for the promotional product and/or the regular of several approaches to segmentation through con- ailab v a cop product’s availability is limited, then whether a cus- joint analysis.) For our model, one can use conjoint

is tomer will get a discounted upsell offer does depend analysis to estimate the reservation prices of target , this on the inventory levels and the time until the end of and nontarget segments, and cross-segment probabil- the season. ities can be estimated in the process as well. uted policies Our numerical results indicate that the beneﬁt of ib using customer purchase information is low when the Acknowledgments distr ﬁrm can dynamically adjust the price and the dis- The authors thank the associate editor and three anony-

mission count. Likewise, when the ﬁrm needs to use a static mous referees for their comments, which helped to improve and the paper. per price and a static discount throughout, the beneﬁt to

ticle the firm from using customer purchase information and ar is low. On the other hand, if the firm needs to use a References static price but can adjust the discount levels dynam- ights Adams, W. J., J. L. Yellen. 1976. Commodity bundling and the bur- this r ically, the use of purchase information is highly bene- den of monopoly. Quart. J. Econom. 90 475–498. to ficial. Our numerical analysis also indicates that even Andrews, K. 1999. Extending upselling and cross-selling efforts. though dynamic discounting decisions bring mod- Target Marketing 22(November) 36–40, 94. Aviv, Y., A. Pazgal. 2005a. Optimal pricing of seasonal products including

yright est improvements over static decisions, setting prices in the presence of forward-looking consumers. Working paper, dynamically seems to have a more signiﬁcant effect Olin School of Business, Washington University, St. Louis, MO. cop on proﬁts. Aviv, Y., A. Pazgal. 2005b. A partially observed Markov decision mation, Given the prevalence of upselling among catalog process for dynamic pricing. Management Sci. 51 1400–1416. or

holds Bitran, G. R., R. Caldentey. 2003. Commissioned paper: An

inf and online retailers and the wealth of customer data overview of pricing models for revenue management. Manu- available to such retailers, data-driven methods that facturing Service Oper. Management 5 203–229. help ﬁrms make better upselling decisions are likely Bitran, G. R., S. V. Mondschein. 1993. Pricing perishable products: to have an impact in practice. In this study, we An application to the retail industry. Working paper, Sloan School of Management, MIT, Boston, MA. INFORMS Additional focused mainly on obtaining insights into the issue Bitran, G. R., S. V. Mondschein. 1997. Periodic pricing of seasonal of upselling. A further line of research would be to products in retail. Management Sci. 43 64–79. develop models with more relaxed assumptions (e.g., Del Franco, M., P. Girard, L. Santo. 1999. Operations benchmark allowing multiple promotional products, and pric- ’99. Catalog Age 16(May) 77, 78, 80, 82, 105. ing ﬂexibility for regular products) and to develop Elmaghraby, W., P. Keskinocak. 2003. Dynamic pricing in the presence of inventory considerations: Research overview, cur- and evaluate heuristic methods amenable for use in rent practices and future directions. Management Sci. 49 practice. For such application-oriented research it is 1287–1309. Aydin and Ziya: Pricing Promotional Products Under Upselling 376 Manufacturing & Service Operations Management 10(3), pp. 360–376, © 2008 INFORMS

Elmaghraby, W., A. Gülcü, P. Keskinocak. 2008. Designing opti- Miller, P. 1995. Fine-tuning upsell technique. Catalog Age 12(July) 61. mal preannounced markdowns in the presence of rational cus- Monahan, G. E., N. C. Petruzzi, W. Zhao. 2004. The dynamic pric- tomers with multiunit demands. Manufacturing Service Oper. ing problem from a newsvendor’s perspective. Manufacturing Management. 10(1) 126–148. Service Oper. Management 6 73–91. Ernst, R., P. Kouvelis. 1999. The effect of selling packaged goods on Muller, A., D. Stoyan. 2002. Comparison Methods for Stochastic Models inventory decisions. Management Sci. 45 1142–1155. and Risks. Wiley, New York. Ferriolo, S. 2003. When less isn’t more. Catalog Age 20(January) Netessine, S., S. Savin, W. Xiao. 2006. Revenue management 38–39.

.org/. through dynamic cross-selling in e-commerce retailing. Oper. Gallego, G., G. van Ryzin. 1994. Optimal dynamic pricing of inven- Res. 54 893–915. ms tories with stochastic demand over ﬁnite horizions. Manage- author(s). Porteus, E. L. 2002. Foundations of Stochastic Inventory Theory. or ment Sci. 40 999–1020. Stanford University Press, Stanford, CA. .inf the Green, P. E., A. M. Krieger. 1991. Segmenting markets with conjoint Stremersch, S., G. J. Tellis. 2002. Strategic bundling of products analysis. J. Marketing 55 20–31. and prices: A new synthesis for marketing. J. Marketing 66 to nals Gurler, U., Z. Bulut, A. Sen. 2005. Bundle pricing of inventories with 55–72. stochastic demand. Extended abstract, 2005 M&SOM Conf., Vriens, M., M. Wedel, T. Wilms. 1996. Metric conjoint segmenta- tesy Northwestern University, Evanston, IL. tion methods: A Monte Carlo comparison. J. Marketing Res. 33 Hanson, W., K. Martin. 1990. Optimal bundle pricing. Management 73–85. http://jour cour Sci. 36 155–174. Yadav, M. S., K. B. Monroe. 1993. How buyers perceive savings in a at a Lariviere, M. A., E. L. Porteus. 2001. Selling to the newsvendor: bundle price: An examination of a bundle’s transaction value.

le An analysis of price-only contracts. Manufacturing Service Oper. J. Marketing Res. 30 350–358. as Management 3 293–305. Zhang, D., W. L. Cooper. 2005. Revenue management for parallel y

ailab Maglaras, C., J. Meissner. 2006. Dynamic pricing strategies for ﬂights with customer-choice behavior. Oper. Res. 53 415–431. v a cop multi-product revenue management problems. Manufacturing Ziya, S., H. Ayhan, R. D. Foley. 2004. Relationship among three

is Service Oper. Management 8 136–148. assumptions in revenue management. Oper. Res. 52 804–809. , this uted policies ib distr mission and per ticle and ar ights this r to including yright cop mation, or holds inf INFORMS Additional