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Optimizing E-tailer Profits and Customer Savings: An Online Dynamic Bundle Pricing Model
Yuanchun Jianga,b Jennifer Shangb Chris F. Kemererb Yezheng Liua,c a
School of Management, Hefei University of Technology, Hefei, Anhui 230009, China
b
The Joseph M. Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA c
Key Laboratory of Process Optimization and Intelligent Decision Making, Ministry of Education, Hefei, Anhui 230009, China
August 2009
Helpful comments on earlier versions of this manuscript were received from W. Chang, S. Daniel and G. May. This work was partially supported by the National Science Foundation of China (Project No.70672097) and the State Key Program of the National Natural Science of China (Project No.70631003).
Optimizing E-tailer Profits and Customer Savings: An Online Dynamic Bundle Pricing Model ABSTRACT Online retailing (“e-tailing”) provides an opportunity for new pricing options that are not feasible in traditional retail settings. This paper proposes a dynamic pricing strategy from the perspective of bundling to derive added savings for customers while maximizing profits for etailers. Given product costs, posted prices and customers’ reservation prices, we propose a nonlinear mixed-integer programming model to increase e-tailers’ profits and enhance customers’ savings. We next extend our dynamic bundle pricing model to accommodate (a) customer budget constraints and (b) e-tailers’ coupons. The computational results suggest that the proposed model not only attracts more customers to buy products at the bundled prices, but also increases profits for the e-tailers.
KEY WORDS AND PHRASES: e-tailing, e-commerce, bundling, dynamic pricing, reservation price, multi-stage process, customer budget, coupons, nonlinear mixed-integer programming model.
1 Introduction The past decade has witnessed an astonishing growth of Internet retailing. Online shopping has become a daily phenomenon for some consumers, with US Internet sales growing to $141.3 billion in 2008, and estimated to reach $156.1 billion in 2009 [14]. This upward trend is expected to continue over the years to come, and, of course, such rapid growth attracts competition. For instance, when a customer is interested in buying a laptop computer, he/she can find one on every website of America’s top 10 Internet retailers [27]. Such Internet retailers (hereafter “e-tailers”) need to continue to look for a competitive edge to both attract new customers and to entice customers to spend more per visit to the website. In this paper we offer an online dynamic bundle pricing (ODBP) model for e-tailers to take advantage of the real-time information available from tracking customers’ decision processes during online purchases. We offer e-tailers a dynamic pricing scheme and provide a price schedule for online shoppers so as to enhance consumers’ savings and maximize e-tailers’ profits in a manner not available to bricks and mortar retailers. Customers’ online shopping behavior is appropriately modeled as a multi-stage process [10]. They sequentially add products to their shopping carts and often buy multiple products in one transaction. Likewise, after placing a few products in the shopping cart they may choose to remove certain items. For such a multi-stage online shopping environment we propose an adaptive profitable pricing model feasible across stages. Once the shopping cart is updated the online system will generate a new recommendation list to help customers find additional products they might desire. Then, for each suggested item it calculates a bundle price by combining the new product with those in the cart. Since the bundle price would be inherently cheaper than the individually posted price,
customers can attain additional savings if they buy more products in one transaction from the same e-tailer. We develop three models under different circumstances: i) customers do not have budget limits and online e-tailers do not offer coupons (base ODBP model); ii) customers have budgets (ODBP_B model); and iii) customers have budgets and online e-tailers offer coupons (ODBP_BC model). To apply the proposed models in the required online environments we develop heuristic methods to quickly solve the models and to provide real-time information for customers to make purchasing decisions. Because customers often have different preferences and valuations for the products, we examine e-tailers’ profits and customers’ savings when customers’ reservation prices follow different distributions, and investigate the degree to which our models can improve profitability over traditional e-tailing strategies. Our results confirm that the proposed approach is a “win-win” strategy as it provides both more gains for e-tailers and more savings for customers. And, the proposed method guarantees the same price schedule regardless of the order in which customers add or remove products from the shopping cart. Our results also show that the ODBP strategy dominates the common retailing strategy under various customers’ reservation price distributions. In particular, customers’ savings and e-tailers’ profits grow if customers buy more products in one transaction. Additionally, the second and third models, with consideration of customers’ budgets and etailers’ coupon promotions, provide e-tailers with a decision aid as to whether to offer coupons based on customers’ profiles in commercial operation. The contributions of our proposed models are threefold: 1. Our models integrate customers’ preferences, customers’ savings and e-tailers’ profits. Compared with existing methods which explore the three aspects independently, the proposed models offer practical benefits in attracting more customer spending by
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incorporating customers’ preferences and savings. However, since the optimization models aim to maximize e-tailers’ profits, the discounts offered to customers will not come at the expense of the e-tailers’ earnings. 2. Traditional pricing models regard customers’ purchasing behavior as a buy-or-notbuy one-stage decision process. Our models more realistically allow customers to explore as many stages as they please, in terms of the number of products and the variety of products. By employing the ODBP model e-tailers can instantaneously provide attractive prices at each stage based on the items preferred by the customer. Incorporating such a real-time pricing capability based on product portfolio significantly enhances the information available to customers and provides better customer service, especially as compared to non-online retailing. 3. The heuristic method developed in this paper advances the viability of real-time online pricing. It achieves quasi-optimal solutions in a negligible time, and enables the optimization models to respond quickly and satisfy the requirement of an online environment. Therefore, by providing real-time information for various scenarios the heuristic approach helps customers make better decisions. The rest of the paper is organized as follows.
In
§ 2 we review the literature of
recommendation systems and pricing strategies and identify key contributions of our model. § 3 proposes a nonlinear mixed-integer programming model to solve the dynamic bundle pricing problem, and a numerical study is conducted in § 4 to examine various scenarios in the ODBP problem. § 5 extends the ODBP model to integrate customers’ budgets and e-tailers’ coupons, and conducts the numerical study.
§ 6 provides a discussion about the application of the
proposed models, and a summary, conclusions, and future research are given in § 7. 2 Problem Introduction and Literature Review 2.1 Problem Introduction Customer preferences and product prices have been documented as two main factors affecting customers’ purchasing decisions [7]. E-tailers often choose among several cross-selling 3
strategies to motivate customers to make more purchases through achieving additional savings. The cross-selling tactics offer customers intending to buy one product a recommendation list consisting of more products. For example, online recommendation systems (ORS) develop customers’ preference models and cross-sell products that customers might favor [21]. Another popular cross-selling device is the bundling strategy which decides whether the products should be sold in unbundled, purely bundled, or mixed bundled form, and then establishes the best price to maximize e-tailers’ profits.1 These strategies are more likely to offer customers products that they desire and to encourage customers to buy multiple products in one transaction. However, several obstacles exist when applying these strategies in business. First, in practice the majority of the ORSs do not take into account the economic incentives of customers and etailers. The ORS predictions of customers’ purchasing decisions tend to be based solely on customers’ previous online behavior [4]. While useful, customers’ prior preferences are not the only factor that affects their choices, and customers’ favorites may not be the ones from which e-tailers could derive maximum profits. Second, the choice of products to cross-sell is often established offline by e-tailers before each selling season. Customers can accept or reject the products offered, but do not have the opportunity to determine the contents of the portfolio. In practice it would be beneficial to allow customers the flexibility to bundle their own favorite products, but traditional fixed portfolios do not take advantage of the dynamic opportunities available online. For example, the potential for real-time pricing discounts is not made available to customers who may be looking for better deals [24]. In an effort to find more practical approaches, newly developed recommendation systems have started to consider customers’ savings and e-tailers’ profits [30]. Dynamic cross-selling 1
The unbundling strategy prices and offers products as separate items only. The pure bundling strategy prices and offers products only as a bundle and not as individual items. The mixed bundling strategy prices and offers bundles as well as the individual items [33].
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strategies and customized bundle pricing approaches have been proposed to enhance e-tailers’ sales and profits.
In the customized bundle pricing problem modeled by Hitt and Chen
customers under a fixed price are allowed to form a bundle by selecting preferred items from a list of available products [12]. Dynamic cross-selling strategies recommend additional products with price discounts when customers plan to buy only one product initially. Netessine et al. show that e-tailers’ profits are maximized when customers buy the extra products proposed [24]. The existing methods provide practical cross-selling strategies to attract more purchases; however, as pointed out by Elmaghraby and Keskinocak [5], the extant literature has not fully incorporated pricing strategies into the online environment. And, conversely, customers’ online browsing and purchasing processes are rarely considered in the current pricing literature. This leads to several limitations. First, without incorporating the perspective of customers’ preferences and savings, as seen in shopbots and many recommendation systems, the systems designed to maximize e-tailers’ profits are less capable of turning online browsers into shoppers, and thus are less likely to result in sales. Although shopbots could derive savings for customers, the products they locate may not be customers’ favorites. On the other hand, those systems that recommend products to maximize profits for e-tailers often do not give due consideration to customers’ savings, and thus it is hard to persuade customers to purchase. Second, the number of products in a bundle in these prior models is pre-specified by retailers ─ customers can only buy a bundle of specific size if the e-tailer offers such an option. However, online shoppers are often interested in knowing the price of different combination of product types and numbers and a more comprehensive model is required to capture this possibility [37]. Although Hui et al. extended the customized bundle pricing problem by allowing e-tailers to
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provide multiple versions of information goods [13], they focus on marginal cost when determining the optimal number of products in the bundles, without considering customers’ savings. Third, the traditional dynamic cross-selling model requires each bundle to consist of exactly two products (e.g., an appliance and an extended warranty). The tied product is established dynamically according to the products customers have bought, and customers can achieve savings only if they buy the tied products. The tied products are selected solely from the etailers’ perspective and the customers will not receive extra savings if they buy additional un-tied products [24]. In terms of actual commercial implementations e-tailers have, to date, implemented several “naive” pricing strategies to encourage customer purchases. For example, the everyday-lowprice promotion strategy of Amazon.com provides a 5% discount to cross-sell the book “The 7 Habits of Highly Effective People” when customers buy the book “How to Win Friends & Influence People”.2 However, as shown in Figure 1 (b), the discounted price is associated with the specific product only. Regardless of other product types or quantity chosen, customers will not gain further savings even if they continue to add more products like the book “Outliers: The Story of Success” to their shopping cart. Insert Figure 1 Here
Since customers are the key to e-tailers’ survival in an online market various approaches have been studied to attract new customers and to maintain old ones. For example, Fan et al. developed a model to examine optimal advertising and pricing strategies for media providers to attract customers [6]. Bapna et al. employed auction-based models to price online services and
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See Figure 1 (a); http://www.amazon.com/How-Win-Friends-Influence-People/dp/0671027034/ref=sr_1_1?ie= UTF8&s=books&qi d=1244563423&sr=8-1 accessed on August 25, 2009.
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to allocate the services based on customers’ budgets [3]. Kohli et al. maintain that online customers’ satisfaction depends highly on cost- and time-savings [19]. Among the available tactics, online recommendation systems and pricing strategies are two effective methods that are gaining acceptance by e-tailers. This section reviews the theoretical and practical models of both. 2.2 Online recommendation systems (ORS) literature review An ORS is a decision aid that analyzes customers’ prior online behavior and suggests products to meet the needs of a particular customer [20]. Most ORSs gather data to extract information and to understand customers’ preferences and then recommend the products most likely to be purchased by the specific customer based on his/her preferences as expressed through their online behavior [1]. To improve customer acceptance of an ORS, Qiu et al. studied the design issue of recommendation systems to enhance customers’ shopping experience [25], while Wang et al. tested the impact of ORS’ explanatory power on customers’ trust in the suggested products [35]. Robert et al. designed a shopbot to find product portfolio for customers to save [28]. However, a limitation of their system is that the products recommended are not based on customers’ preferences, but rather are based on product prices and e-tailers’ promotion strategies. Chen et al. [4] proposed a recommendation system to enhance e-tailers’ profits. However, their model does not take into account customer savings. In summary, in traditional ORS research e-tailers’ profits, customer preferences and customer gains have not been integrated, and thus the current ORSs are less likely to translate the recommended products into sales than would a system that accommodated all three dimensions [34, 36]. These findings motivate us to incorporate e-tailers’ profits, customers’ preferences and savings when developing new strategies for e-tailers.
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2.3 Dynamic pricing and bundle pricing in revenue management Dynamic pricing, such as quantity discounts, has been adopted in a number of industries as it can be an important strategy that aids customer retention and therefore helps to create a competitive advantage for a firm [29]. Traditionally, price is established based on cost, demand, inventory level, and a variety of other factors [5]. Compared with a traditional environment, however, price in the online environment can be set dynamically to match competitors’ prices and customers’ preferences [18]. E-tailers can change prices, either across customers or across products, by dynamically updating the posted prices, selling product via auctions, and by offering quantity discounts [15]. For example, to increase sales volume, Kauffman et al. modeled a group buying discount problem in which e-tailers could drop a product’s unit price as more customers place orders [16]. And, customers with different attitudes towards piracy may be charged with different prices for the same digital information good such as music and video [17].3 Finally, bundle pricing, which aims to sell two or more products jointly, is an attractive marketing practice [26]. It can offer monetary savings for customers, enhance product differentiation, gain competitive advantage, and increase profits for firms. Bundle pricing research helps determine whether products should be sold as pure- or mixed-bundling, and how to price them. Venkatesh and Mahajan [33] propose a probabilistic approach to price a bundle using multiple criteria. They also combine marginal costs and different degrees of complementarity and substitutability to determine the best bundling strategies [32]. Based on customers’ reservation prices, McCardle et al. [22] propose a pricing model for fashion bundles. 3
Note, however, that retailers must be careful to offer a reasonable explanation for their variable pricing methods. Otherwise, they may face a negative public reaction. For example, in September 2000 Amazon.com adopted a differential pricing strategy by which different customers were charged different prices for the same product according to their profiles. This experiment failed and was withdrawn by Amazon because many customers deemed it unfair [11].
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In general, to maximize profits most researchers have focused on pricing for individual products and bundles, subject to constraints of customer demand, arrival process, reservation price, and supply information [2, 8]. 3 The Online Dynamic Bundle Pricing (ODBP) Model 3.1 Distinctive features of our ODBP model The ODBP model developed in this research contains a number of advances over prior work. First, the ODBP model emphasizes motivating customers, since simply establishing strategies to maximize e-tailers’ profits without inspiring customers to participate more is less likely to improve sales, ceteris paribus. Given the posted prices of the recommended products, our model establishes optimal prices, subject to the constraint of increasing customer savings, which is expected to entice more purchases. Second, traditional pricing models regard customers’ purchasing behavior as a one-stage process, where they decide to buy or not to buy a product or a bundle as a single decision. However, online shopping has been reported to more typically be a multi-stage process [10]. If traditional models are applied to determine the bundle price at each stage, price violations are likely to occur frequently – that is, the bundle price of the products in the shopping cart may be greater than the sum of the individually posted prices; and the bundle price depends on the sequence of the products chosen. The revenue management and marketing science literature that study customized bundle pricing [12,36] and dynamic cross-selling problems [24] are related to our research. However, in the traditional dynamic cross-selling method, the cross-sold products may not be the customers’ favorites and customers could not achieve savings once they reject these products. In our model customers take a more pro-active approach when shopping online. The products involved in one transaction are not homogeneous and e-tailers are not required to preset the
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number and types of products to be included in the bundles for customers. Our model allows for shoppers to realistically have flexibility and choice in terms of when and what to put in their shopping cart. The model incorporates the customer’s view and seeks savings for customers, thereby enhancing customer satisfaction with the likely concomitant increase in e-tailers’ sales. Compared with the dynamic cross-selling problem, our bundles are formed by customers, and customers are guaranteed to achieve additional savings every time a new item is added to the cart. 3.2 Foundational Assumptions In this section we formulate the Online Dynamic Bundle Pricing (ODBP) problem as a nonlinear mixed-integer programming model for e-tailers. Before describing the details of our model we provide the fundamental assumptions made in this paper. The model is designed to help increase sales and customer satisfaction in an online retailing environment. It is assumed that e-tailers have sufficient transaction records and other information to generate recommendations and that the products in the recommendation list reflect the customers’ penchant for such products. This assumption is supported by the research in online recommendation systems, whereby a customer’s online behavior (e.g., browsing web pages, updating shopping carts) reflects his/her needs and desires [1]. Therefore, the products recommended according to customers’ online behavior are assumed to meet their needs. Second, consumers’ reservation prices for a bundle of goods are independent.4 The reservation price of a bundle is the sum of the reservation prices of individual products in the bundle. Customers’ purchasing decisions are governed by their surplus utilities, i.e. the differences between
4
This is a common assumption in the bundle pricing and ORS research [7, 36]. For the independently valued products a consumer’s reservation price for a bundle satisfies the assumption of strict additivity and is equal to the sum of his/her reservation prices of the individual products. For products with dependent reservation prices a consumer’s reservation price for a bundle would be superadditive or subaddititive. Details of the computation of the reservation prices for bundles can be found in Venkatesh et al. [32].
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reservation prices and the prices they are charged.5 Third, the individual price posted online gives the highest possible profits when selling the product alone. Methods for establishing posted prices can be found in McCardle et al. [22], who have included the costs of manufacturing, inventory, and procurement, among others. 3.3 Model Requirements The online shopping environment dictates that a practical dynamic bundle pricing model satisfies the following requirements. First, the bundle price is not dependent upon the sequence of adding products to the shopping cart. For example, customers must be charged the same price in both of the following circumstances. (1) Select a $8.70 “How to Win Friends & Influence People” book after a $14.83 “Outliers: The Story of Success” book is already put in the shopping cart. (2) Select a $14.83 “Outliers: The Story of Success” book after a $8.70 “How to Win Friends & Influence People” book is already put in the cart. A naive strategy of “5% discount on the next product you purchase” would return with different bundle price when choosing one before the other due to a different base price being applied to the discount rate. Second, price violations are not allowed. That is, if the bundle price of the shopping cart is greater than the sum of the posted prices ─ a price violation, then bundling becomes meaningless and customers will not be interested in purchasing at all. Moreover, if the additional charge when adding a product to the shopping cart is greater than the posted price of that product, even if the bundle price of the shopping cart is less than the sum of posted prices, a rational customer will check out the products in the cart first, and then decide whether to buy the recommended product with the posted price due to no price advantage by including it in the bundle. Third, when customers remove products from the shopping cart, the price of the shopping cart
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Based on the first assumption we assume that customers will buy a product if the price of the product is at or below their reservation price, which is a common assumption in the revenue management literature [12,36].
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needs to stay rational. For example, suppose the shopping cart consists of three products: “How to Win Friends & Influence People”, “Outliers: The Story of Success”, and “The 7 Habits of Highly Effective People”. If the customer decides to remove “Outliers: The Story of Success” from the shopping cart, the bundle price of the reversely updated shopping cart should equal the bundle price when customers put “How to Win Friends & Influence People” and “The 7 Habits of Highly Effective People” to the shopping cart sequentially. Traditional implementations of pricing strategies such as customized bundling and dynamic cross-selling are based on fixed discount rates or fixed portfolio size and are not designed to satisfy these three model requirements. We thus propose a new model to dynamically determine the bundle price for online shoppers during their multi-stage decision process. 3.4 The Proposed Model Suppose an e-tailer has N products and M potential customers. Each product has a fixed cost and a posted price. Each customer has a reservation price for each product. Suppose I products are already in the shopping cart, GS = {gS1 , …, gSi, …, gSI}, the corresponding posted prices, costs and reservation prices are {pS1, …, pSi, …, pSI}, {cS1, …, cSi, …, cSI}, {rSm,1, …, rSm,i, …, rSm,I}, m = 1, 2, …, M, i = 1, 2, …, I. The bundle price of the shopping cart is pS, and pS = pS1 if there is only one product in the shopping cart. Based on the products in GS, additional J products are recommended, GR = {gR1, …, gRj, …, gRJ}. The corresponding posted prices, costs and reservation prices are {pR1, …, pRj, …, pRJ}, {cR1, …, cRj, …, cRJ}, {rRm,1, …, rRm,j, …, rRm,J}, j = 1,2, …, J. For each recommended product gRj in GR, we combine it together with the products in GS as a bundle, {gS1,…, gSi,…, gSI, gRj }, and calculate the bundle price to persuade customers to buy them in one transaction.6
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We assume that ORSs recommend individual products and customers add one product to shopping cart at a time. For the cases where recommendation list contains product portfolios and customers are allowed to simultaneously add multi-products to the
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Insert Table 1 Here Table 1 outlines the basic notations necessary to formulate the dynamic bundle pricing strategy as a nonlinear mixed-integer programming model. The optimal model for the online dynamic bundle pricing strategy (base ODBP model) is given as follows. M
I
m1
u 1
max ( p ( cuS c Rj )) X m
(1)
s.t. I
[( rmS,u rmR, j p) (rmR, j p Rj )] X m 0 , m 1,..., M
(2)
[( rmS,u rmR, j p) (rmS,i piS )] X m 0 , i 1,..., I , m 1,..., M
(3)
u 1 I
u 1 I
( rmS,u rmR, j p) X m 0 , m 1,2,..., M
(4)
p p S p Rj 0
(5)
p pi piS 0 , i 1,..., I
(6)
u 1
I
p cuS c Rj
(7)
p puS p Rj
(8)
X m 0 or 1 , m 1,..., M
(9)
u 1 I
u 1
The objective function (1) maximizes the total profit of the e-tailer when recommending product gRj to the customers who have already had the products gSi in the shopping cart, i = 1, 2, …, I. The profits of the e-tailer are the total profits obtained from the customers who would add gRj to the shopping cart. The profit obtained from each customer is the difference between the bundle price and the total cost. Constraints (2), (3) and (4) together determine whether a customer would buy the bundle at the price p. The sum of a customer’s reservation price for the products in the shopping cart is shopping cart, our model is still capable of obtaining the bundling prices by bundling the product portfolios with the products in the shopping cart.
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I
represented by
rmS,u and u 1
I
r u 1
S m ,u
rmR, j p is customer m’s surplus utility of buying the bundle
{gS1,…, gSi,…, gSI, gRj } at price p. Constraints (2) and (3) make sure that each customer maximizes his/her surplus utility. To attract customers to buy gRj, the surplus utility derived from the bundle price must be larger than that generated by separately buying the products in the bundle with the posted prices. If the surplus utility of the bundle is less than that of gRj, customers would not buy gRj. If the surplus utility of the bundle is less than that of gSi in the shopping cart, customers would remove gSi from the shopping cart. Customers would buy the bundle only if their reservation prices for the bundle are no less than the bundle price, as shown in constraints (4). If the bundle price is higher than the customer’s sum of all reservation prices in the bundle, no customers will be willing to pay for gRj and the e-tailer will not make additional profits by selling gRj. Constraints (5) make sure that the additional charge, when adding product gRj to the shopping cart, is no more than the posted price of gRj. Otherwise, customers would check out with the products {gS1 , …, gSi, …, gSI}, and buy gRj separately. Besides adding product gRj to the shopping cart, there are additional I cases to form the bundle {gS1 , …, gSi, …, gSI, gRj}: customers may add gSi to the shopping cart which consists of the products {gS1 , …, gSi-1, gSi+1, …, gSI, gRj }, i = 1, 2, …, I. Constraints (6) make sure that the bundle prices for all I + 1 cases are the same. The bundle price is not dependent on the purchasing sequence. Constraint (7) makes sure that the bundle price is no less than the total cost of the products in the bundle. Otherwise, e-tailers will receive no profit by selling the bundle. Constraint (8) makes sure that the bundle price is no more than the sum of the posted price of all products in the bundle. However, given constraints (5) and (6), constraint (8) is redundant, so we will remove it when solving the model. Decision variable Xm denotes whether
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customer m will buy the products in this transaction at the bundle price p. When customer m buys the products Xm equals 1, otherwise, Xm equals 0. Constraints (6) require solving the bundle pricing model repeatedly. If a customer transaction contains more than 10 products the recurring application of the nonlinear mixed-integer programming algorithms may require excessive computation time to reach optimality, and therefore it is computationally prohibitive for the real-time recommendation systems. To resolve this issue we provide a quasi-optimal method to solve the bundle pricing model. Details of the quasi-optimal method are presented in Figure 2. Insert Figure 2 Here In Figure 2, before determining the optimal price for the bundle {gS1 , …, gSi, …, gSI, gRj}, we have to first obtain the optimal prices of p-i, i = 1,2,…,I, which also require repeated execution of I 1
the proposed model. The total number of the nested loop is
v2
I
Cv 1 , which equals the number
of runs needed to arrive at the final bundle price, where ICv is the mathematical symbol of the combination operation. Clearly, this is a time-consuming approach and unacceptable to online customers. Therefore, Figure 3 proposes a heuristic method to determine the quasi-optimal value of p-i which is much more efficient than the quasi-optimal solution given in Figure 2. Insert Figure 3 Here In the heuristic method, we calculate p-v + pv to be a quasi-optimal value of the upper bound of p-i. The heuristic method is based on the following observation. Suppose there are three products: g1, g2, g3 with prices of $10, $100 and $200 respectively, where g1 is the one that has the lowest price. There are three possibilities that a customer can form the bundle {g1, g2, g3}. First, the shopping cart consists of g2 and g3 and the customer adds g1. Second, the shopping cart consists of g1 and g3, and the customer adds g2. And finally, the shopping cart consists of g1 and
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g2, and the customer adds g3. As mentioned earlier, to attract customers to make more purchases, the model seeks to increase customer savings when more items are purchased in one transaction. In the above three cases based on the earlier solutions, suppose the savings customers have received for the two products in the shopping cart are $15, $10, $6, respectively. The upper bounds derived from the three cases are $295, $300, and $304, respectively.7 Thus, $295 is the lowest upper bound of these three.8 With the heuristic method the nested loop will only be executed (I – 1) times to calculate p-i and I (I – 1) + 1 times to calculate p if I is larger than 2. Although solving small-sized optimization problems with optimization software is becoming increasing practicable, a drawback of optimization software is that they are generic tools and solve problems without considering the special features of the problem in question. As a consequence they can often require a relatively long solution time. In an online ordering environment a waiting time of more than a few seconds is unacceptable, and may lead to the loss of customers. Therefore, a near instantaneous solution to customers’ queries is essential. By taking advantage of the unique structure of the online dynamic bundle pricing problem, the proposed heuristic method allows e-tailers to obtain the same optimal solution as that derived by the optimization software, given that the search step length is sufficiently large. Since the proposed heuristic is very efficient it can be executed instantaneously, i.e. the time needed to solve the ODBP model is often negligible. Thus, e-tailers can choose a sufficiently large step length to search and quickly arrive at a near-optimal solution. As shown in Table 3 the heuristic method is able to produce similar solution quality for an eight-product bundle, while taking only 0.1% of the execution time needed by the quasi-optimal method. 7
For example, in the first case, the bundle price of the shopping cart is $285, which is calculated by the sum of the posted price of g2 ($100) and g3 ($200) minus customer savings ($15). Thus, the bundle price of the three products should be less than the sum ($295) of the price of the shopping cart ($285) and the price of product g1 ($10). 8 The three constraints, i.e. the bundle price is less than $295, $300, and $304 respectively, must be satisfied simultaneously. The latter two constraints are redundant once the bundle price is less than $295.
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3.5 An Illustrative Example Figure 4 illustrates the concept, the decision process, and the information flow of the ODBP model. Suppose an e-tailer has eight products (e.g. A, B, C, D, E, F, G, H) for sale and the posted prices for the products are $1, $2, $3, $4, $5, $6, $7, and $8, respectively. Assume that a customer’s reservation prices for the eight products are $0.8, $3, $2.5, $4.3, $4.8, $5.5, $7.3, and $7.5, respectively.9 After the customer logs on to the e-tailer’s website the ORS suggests a list of products {A, B, C} according to the customer’s preference and shopping history. The purchasing decisions may be made due to personal preference, needs, or savings if more than one product’s selling price is smaller than his/her reservation prices. Suppose this customer is a rational shopper who seeks to maximize savings, defined as the posted price minus the marginal price. Note that the marginal price is the change in total price that arises when a product is added to the shopping cart. After the customer adds B to his/her shopping cart, the ORS recommends another list of products {A, C, D} and uses our model to calculate the bundle prices for the three bundles {B, A}, {B, C}, {B, D}. Based on his/her need and budget the customer may either continue to purchase products or check out with product B. For product A the customer will not buy it at the posted price because his/her reservation price is $0.8, which is less than the product’s posted price, $1. However, given that the marginal price as calculated by the proposed model, $0.7, is less than his/her reservation price, $0.8, the customer is motivated to purchase product A with the cheaper price offered through the bundle. In the following step the customer may add product F to the cart in a similar manner.
A reservation price is the maximum price a customer is willing to pay for a product. How to estimate customers’ reservation prices is an important issue that merits separate study. Direct elicitation and indirect estimation are two main methods to point-estimate customers’ reservation prices [34]. Wang et al. [34] further proposed a three-step method, ICERANGE, to elicit customer’s reservation price in ranges. For our purpose we assume that the reservation price is a point estimate from elicitation. If the reservation price is given in a range, one can adopt the value at which customer’s probability of purchase is maximized. 9
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After products A, B, and F have been added to the shopping cart, the customer may decide not to buy product A due to its similarity to product F, and remove it from the cart. In this case the proposed model is applied again to calculate the bundle price of {B, F}. Next, the ORS would recommend products {C, E, H}10 and calculate the bundle price by bundling each recommended product with {B, F}. Note that the price of {B, F} should satisfy the “rational constraint”, i.e. the prices should be the same regardless of the sequence in which the products are added to the cart. Insert Figure 4 Here 4 Numerical Study and Analysis of the Base ODBP model In this section, we conduct a variety of numerical studies to understand the impact of the ODBP strategy from the perspectives of e-tailers and customers. By comparing e-tailers’ profits and customers’ savings we test the effectiveness of the proposed dynamic pricing model versus the traditional static online pricing strategy. We also examine the influence of customers’ reservation prices on both e-tailers and customers. We further investigate the execution efficiency of the quasi-optimal method and the heuristic approach. 4.1 The Data Sets and Experiment Procedure To perform the numerical analysis we first determine the number of products and customers an e-tailer has and simulate the prices and costs of the products, and the reservation price of each customer for each product. Since uniform distributions have been used widely in the study of revenue management [32, 36], we also simulate customers’ reservation prices using a uniform distribution. We assume that customers’ reservation prices for a product follows the distribution
10
Different products in the shopping cart may portray distinct customer characteristics and generate different recommendation lists. After customers remove product A from the shopping cart, the products {B, F} may communicate new customer characteristics and thus extract a different recommendation list.
18
U(u–b, u+b), where u is a random number between $0 and $10, and b is a result of percentage discount of u, i.e. b = u, [0,1]. Without loss of generality we set to 0.2 in our study. The impact of customers’ reservation prices on the e-tailer’s profits and customers’ savings are examined in section 4.3. The cost of a product is assumed to be a random percentage of u. The percentage interval is [0.75, 0.95] in our analysis. Given the reservation prices and product costs, and using McCardle et al. [22] as guideline, we establish the posted price for each product to achieve best profits when selling the product individually on the e-tailer’s website. With the generated products we simulate the e-tailer’s transaction database of 3000 records. Researchers and practitioners suggest that the maximum number of products in one transaction is relatively small and often no more than 12 items [4]. Therefore, in the simulated database the number of products in one transaction follows the uniform distribution U(1,12). The recommendation method used in our study is the item-to-item collaborative filtering technology of Amazon.com [21]. The experiment starts from a transaction with one product. That is, we first randomly select one product from the database and assume it is a customer’s first decision in the multi-stage purchasing process. From this starting point the recommendation system generates a suggestion list from which a product is randomly selected each time to form a two-product bundle which creates a variety of bundles. The ODBP model will determine the optimal price for each two-product bundle and assess the e-tailer’s profits and customers’ savings. Among all the recommended and priced two-product bundles, the (simulated) customer will select a specific one to his/her liking, and move to the next stage, where a new list of recommended products is presented. The transaction analysis for more products continues similarly.
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4.2 Improvement of E-tailer’s Profits and Customers’ Savings In this section we examine the improvement in the e-tailer’s profits and the customers’ savings when the e-tailer adopts ODBP. Without loss of generality the number of customers M is set to 500 and the number of products N is assumed to equal M. In Table 2 the values in the “Unbundling profit” column are the e-tailer’s profits when customers pay at the posted prices and the values in the “Bundling profit” column are the profits generated when customers buy products at the bundle prices. The values listed under “Profit improvement (%)”, are the percentages of profits improved due to the ODBP strategy and are calculated by ((bundling profit – unbundling profit)/unbundling profit). The “Unbundling payout” values are the average expenditures customers would pay based on posted prices, while “Bundling payout” gives the average customers’ spending under the ODBP strategy. The values in the column “Savings” are customers’ average savings when moving from the unbundling strategy to the ODBP strategy. The “New customers (%)” values are the percentage increase in the number of customers who would buy the bundles at the bundle prices, but not buy at the posted prices. Insert Table 2 Here Through the ODBP strategy customers who would not buy the recommended products at the posted prices may be more interested and motivated to purchase at the bundle prices. Therefore, although the unit profit decreases, ODBP increase profits due to the greater sales as shown in Table 2. The e-tailer attracts nearly twice as many customers for the two-product bundles when employing the ODBP strategy as that using the unbundling strategy. Furthermore, the number of new customers has systematically grown with the bundle size, and amounts to 336.8% for the eight-product bundles. Additionally, more products assure more profits ─ for example, the
20
average profit improvement from the eight-product bundles is 5.6 times more than that of the two-product bundles, a clear incentive for the e-tailer to adopt the ODBP model when dealing with potential volume buyers. The e-tailer’s profits present a convincing argument as to the attractiveness of the ODBP strategy. However, the precondition of e-tailer’s profit improvement depends on customers’ willingness to pay for the additional products in one transaction. To show that customers are likely to purchase more following the ODBP strategy, we also display the savings customers may realize in Table 2. Because customers’ purchasing decisions are usually based on product prices after they find what they need, an effective promotion is to show that customers can achieve additional savings if they continue making purchases from the same e-tailer. Table 2 demonstrates that customers can achieve additional savings under ODBP strategy, and the more products bought, the more savings realized. Clearly, rational customers would be motivated to buy more products in one transaction to achieve more savings, ceteris paribus. To meet the requirement of the online real-time environment, the results in Table 2 are derived through the heuristic method which aims at reducing the execution time of the ODBP model. As illustrated in Table 3 the efficiency of the heuristic approach is more distinct when a larger number of products are involved. For the two- and three-product bundles the quasi-optimal method and the heuristic method require essentially the same computation time. However, when more products are under consideration the heuristic method outperforms the quasi-optimal method. The efficiency improvement due to the heuristic method, calculated by ((execution time of quasi-optimal method – execution time of heuristic method)/ execution time of quasi-optimal method), is up to 99.9% (for the eight-product bundles). While improving the execution efficiency drastically, the heuristic method continues to reach the same solution quality as those
21
of the quasi-optimal method. The paired t-test found that there is no significant difference between the optimal prices obtained by the quasi-optimal method and the heuristic approach (pvalue = 0.483). Thus, the heuristic method is chosen for the rest of the numerical analysis. Insert Table 3 Here 4.3 The impact of reservation price on E-tailer’s Profits and Customers’ Savings In this section we investigate the impact of the reservation price on the ODBP strategy. The reservation price is one of the most important factors that influence the bundle price. We have so far assumed that customers’ reservation prices for each product follow a uniform distribution. In this subsection we first examine the impact of the scale of customers’ reservation prices on both the e-tailer and customers (Table 4). Then, we examine the impact of different distributions of customers’ reservation prices (Table 5). Insert Table 4 Here Insert Table 5 Here The range of the uniform distribution, 2βu, measures the deviation of customers’ valuations of the products. A larger β indicates there are more diverse views regarding the value of products, while a smaller β implies that customers’ divergence is less. For example, Figure 5 presents four probability density functions of the uniform distribution U(u–b, u+b) where u is 3.528 and is 0.1, 0.15, 0.25 and 0.3, respectively. Based on the four scales of reservation prices, the optimal prices of the individual products are derived using the method similar to that in McCardle et al. [22] and they are 3.422, 3.475, 3.616 and 3.740, respectively. The areas of regions a, b, c, and d, which are 0.680, 0.564, 0.470, and 0.444, represent the probabilities of customers’ purchase. The decrease of the areas of the four regions indicates that fewer and fewer customers are willing to buy the product at the posted price when the product is sold individually. The increasing number
22
of potential purchasers means that the ODBP strategy has better opportunities to attract more business. Table 4 presents the e-tailer’s profit improvements when is increased from 0.1 to 0.15, 0.25 and 0.3, respectively. When is 0.3 the average profits ($1082.50) for the eightproduct bundles are more than three times the profits ($314.53) when is 0.1. Correspondingly, the discounts provided by the e-tailer must increase in order to attract more purchases when customer heterogeneity increases. Therefore, customers will achieve more savings from buying the products. As shown in Table 4 customers’ average savings when is 0.3 are 3.8 times larger than that when is 0.1 for the eight-product bundles. Insert Figure 5 Here We investigate four cases to examine the impact of different distributions of customers’ reservation prices using the uniform and normal distributions. For the normal distribution customers’ reservation prices for a product are assumed to follow N(u,2), where u is a random number between 0 and 10, and is a percentage of u, = 0.2 u. Case 1 (Normal) and Case 2 (Uniform) examine the e-tailer’s profit improvements and customers’ savings when customers’ reservation prices are normally- and uniformly-distributed, respectively. Case 3 (0.3N&0.7U) and Case 4 (0.7N&0.3U) consider the cases where customers’ valuations for different products follow different types of distributions. In Case 3 we randomly select 30% of the products and assume that customers’ reservation prices for those products follow normal distributions, and customers’ reservation prices of the other 70% of the products follow uniform distributions. In Case 4 customers’ reservation prices of the randomly selected 70% products follow normal distributions, while the other 30% follow uniform distributions. As shown in Table 5 the dynamic bundle pricing strategy dominantly outperforms the unbundling strategy. For example, for the eight-product bundles in Case 4, the e-tailer’s profit improvements and customer’s
23
savings under the ODBP strategy are 869.049 and 3.918 respectively. The e-tailer and customers may obtain even higher benefits under other customer reservation price distributions. 5 Online Dynamic Bundle Pricing with Budget and Coupon In the base ODBP model e-tailers focus on pricing different bundles established by the potential buyers. In practice, e-tailers regularly provide a mixture of promotion strategies, such as “Free shipping”, “Free item”, “Dollar-off”, and “Percentage-off”, to attract customers. The “Dollar-off” coupon, which can be used to reduce the total price of the transaction if the minimum amount is reached, is one of the most popular promotion strategies used by e-tailers. For example, Bestbuy.com often provides a $5 off $75, or a $10 off $200 digital coupon code.11 In addition, customers can set budget limits to determine their willingness and ability to pay for the products. Intuitively, a customer’s budget is influenced by their economic situation and their purchase experiences, e.g., a customer’s budget often decreases during an economic downturn and increases in an upturn. To motivate customers e-tailers can provide greater discounts when lower budgets are predicted, and offer lesser discounts if a higher budget level is projected. Methods used to forecast customers’ budgets within different time frames can be found in Ulkumen et al. [31]. 5.1 The ODBP_BC and ODBP_B models In this subsection we extend the ODBP model to combine the “Dollar-off” coupon and the customer’s budget. Suppose the e-tailer has K types of “Dollar-off” coupons, with {o1, …, ok, …, oK} and {d1, …, dk, …, dK} representing the trigger prices and the corresponding discounts, where dk > dl if ok > ol. For example, (ok, dk) may be a $5 off $75 coupon, where ok = 75 is the trigger price of the coupon, dk = 5 is the corresponding dollar discount, and (0, 0) symbolizes no
11
See http://www.ecoupons.com/coupon-code/Best-Buy for more coupon information published by Bestbuy.com.
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coupons have been received. The coupon in the shopping cart is represented as (oS, dS) and (o-i, d-i) is the coupon received when a customer adds the products {gS1 , …, gSi-1, gSi+1, …, gSI, gRj} to the shopping cart, where o-i = d-i = oS = dS = 0 if there is only one product in the shopping cart. The budgets of the M customers are {b1, …, bm, …, bM}. The optimal model for the ODBP strategy with budget and coupon (ODBP_BC model) is as follows:
M
I
K
m1
i 1
k 1
max ( p ( ciS c Rj ) Yk d k ) X i
(10)
s.t. K
[ Rm ( p Yk d k ) (rmR, j p Rj )] X m 0 , m 1,..., M
(11)
[ Rm ( p Yk d k ) (rmS,i piS )] X m 0 , i 1,..., I , m 1,..., M
(12)
( Rm ( p Yk d k )) X m 0 , m 1,2,..., M
(13)
k 1 K
k 1 K
k 1
K
p Yk d k ( p S d S ) p Rj 0
(14)
p Yk d k ( pi d i ) piS 0 , i 1,..., I
(15)
k 1 K k 1 K
I
p Yk d k cuS
(16)
p puS p Rj
(17)
( p Yk d k bm ) X m 0 , m 1,2,..., M
(18)
k 1 I
u 1
u 1 K
k 1
( p ok )Yk 0 , k 1,..., K
(19) (20)
( p ot )(ot ok )Yk 0 , t , k 1,..., K , t k I
Rm rmS,u rmR, j , m 1,..., M
(21)
u 1
X m 0 or 1 , m 1,..., M
(22) (23)
Yk 0 or 1 , k 1,..., K
With the digital coupon a customer’s actual expenditure is the difference between the bundle price and the dollar discount. In the ODBP_BC model constraints (11) – (16) are similar to
25
K
constraints (2) – (7) where p is replaced by p Yk d k . Constraint (17) makes sure that the k 1
bundle price is smaller than the sum of the posted prices. Constraints (18) ensure that customers’ actual expenditure is smaller than their budget, as otherwise customers cannot afford the products. Constraints (19) establish that customers may receive a coupon only when the bundle price is not smaller than the trigger price of the coupon. Also, except the chosen coupon, no other coupons may be activated by the bundle price and result in a better discount. Thus constraints (20) confirm that no more than one coupon will be received per transaction. Constraints (21) define customers’ reservation prices for the bundle. The binary variable Yk denotes whether customers will receive a coupon (ok, dk). And Yk equals 1 when the e-tailer offers the coupon; otherwise, Yk equals 0. We revise the heuristic methods proposed in Figure 3 to solve the above pricing model with budget limits and coupon offers. Constraints (14), (15), and (17) collectively form the upper bound of the optimal price while constraint (16) establishes the lower bound. When using the fixed step length to search for optimal price from the upper bound to lower bound, four decisions need to be made successively at each alternative price point. First, is the profit derived from the price point larger than the maximum profit derived so far? Second, which coupon can be activated at the price point? Third, is the price point minus the discount provided by the coupon larger than the lower bound? Fourth, is the profit derived from the price point and the coupon larger than the current maximum profit? If the answer of the fourth judgment is yes, the price point together with the coupon is selected as the newest solution of the model. The decision logic flow diagram at each price point is presented in Figure 6. Insert Figure 6 Here The literature on coupon promotion points out that not all customers actively seek out
26
coupons from e-tailers as customers’ decisions to use coupons are dependent on the cost of using coupons, the savings obtained, and customer’s price-sensitivity [9, 23]. Therefore, e-tailers can decide whether to distribute coupons according to what is known about the customers. The ODBP_BC model can accommodate either case, as follows. In the ODBP_BC model the dollar discount of the coupon is equivalent to the savings derived from the bundle price. If e-tailers do not provide coupons, the ODBP_BC model can be simplified to an ODBP_B model, by adding the following constraints to the base ODBP model: ( p bm ) X m 0 , m 1,2,..., M
(24) .
The ODBP_B model offers e-tailers the bundle price equivalent to that derived from the ODBP_BC model minus the value of the coupon when a coupon is available. The solution of the ODBP_B model (bundle prices) can derive almost the same profits and savings relative to that of the ODBP_BC model (bundle prices and coupons). 5.2 Numerical study of ODBP_B and ODBP_BC models In this subsection we study the benefits to both e-tailers and customers when coupons are offered and budget constraints are considered. We first examine the impact of the ODBP_BC model where customers have budget limits and the e-tailer offers coupons for promotion. Three coupons, {(1, 15), (3, 30), (5, 45)}, are used in our study. Customers’ budgets are assumed to follow a normal distribution N(u,2), = 0.2 u. This subsection examines four cases where u equals 20, 30, 40, and 50, respectively. We first examine the impact of customers’ budgets on the e-tailer’s profits. Insert Table 6 Here Limited by their budgets, customers may choose not to buy certain products even if their reservation prices are higher than the offered prices. As shown in Table 2 and Table 6, the
27
e-tailer’s profits are obviously smaller than that when customers have sufficient budgets to buy whatever they prefer. In Case 1 and Case 2 the profits derived from the transactions with more products decrease because customers have limited budgets at their disposal. An interesting finding from Table 6 is that the percentage improvement of the e-tailer’s profits increases as u decreases from 50 to 20. For example, the profit improvement for the eight-product bundles is 356.8% when u is 20, but it is 209.3% when u is 50. This indicates that the proposed method will play a more important role in enhancing e-tailers’ profitability when customers’ purchasing power decreases, as in an economic downturn. In our example customers may receive one of the three coupons after they add products to the shopping cart. The probabilities of receiving coupons corresponding to the number of products in one transaction are presented in Table 7. Customers may receive different kinds of coupons according to the products in the shopping cart. When customers buy fewer products in one transaction, the total price of the transaction may be insufficient to activate any coupons and therefore customers are unlikely to receive coupons. However, as the number of products in the cart increases, customers have better chances to receive coupons which lead to more savings. In Table 7 the expected savings from coupons increase as the number of products in one transaction increases. Naturally, this is also an effective strategy to attract more purchases. Insert Table 7 Here Figure 7 and Figure 8 demonstrate customers’ actual expenditures and the e-tailer’s profits in the ODBP_BC and ODBP_B models. Customers’ budgets follow a normal distribution N (40, 8). As shown in Figure 7 and Figure 8 the customers’ expenditures and the e-tailer’s profits are approximately the same in the two models. By identifying the minimum price hike necessary to maintain the e-tailer’s profits, the ODBP_BC model helps to offset the loss of profits due to
28
coupon offering. Correspondingly, even though customers can redeem online coupons, their savings are comparable in both the ODBP_B and ODBP_BC models. This is because we design the model from the perspectives of e-tailers and the main goal is to maximize their profits, while seeking customers’ savings. Therefore, under normal circumstances, customers have to pay higher bundle prices in the ODBP_BC model. E-tailers can employ the ODBP_B model to attract customers through direct discount if they decide not to offer coupons. The models provide e-tailers the flexibility of deciding whether to offer coupons based on customers’ profile in commercial operation. Insert Figure 7 Here Insert Figure 8 Here 6 Application of the Proposed Models This section provides guidelines as to how the proposed models may be applied with and without coupons. Traditionally it has been suggested that there are three types of relationships between products: substitutes, complements and independent products. In product recommendations all three relationships may be encountered. Consider an example of a customer shopping for computer products at Amazon.com. After the customer adds an “HP Laptop” and “Microsoft Office Student” to their shopping cart the recommendation system may recommend, among others, an “Acer Laptop” (substitute for the “HP Laptop”), a “Targus Notebook Case” (complement of “HP laptop”), an “Apple MP3 Player” (independent of the products in the shopping cart), and “Office All-in-One” (substitute for “Microsoft Office Student”). Naturally, in contrast to the complements and independent products, customers generally buy only one of the substitutes at a time but not both. Therefore, the following two cases should be treated differently when applying the proposed model.
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In Case 1 the recommended product is a substitute to the product in the shopping cart. If product gRj is a substitute for gSI, the proposed model should calculate the bundle price of {gS1 , …, gSi, …, gSI-1, gRj}. The recommendation strategy will be similar to “Frequently Bought Together”, where the product portfolio is {gS1 , …, gSi, …, gSI-1, gRj}. In Case 2 the recommended product is independent or complementary to the products in the cart. In this case the proposed model can be employed directly to calculate the price for the bundle, consisting of the recommended product and the products in the shopping cart. The recommendation strategy for this case would be similar to “Customers Who Bought Items in Your Shopping Cart Also Bought” used by Amazon.com. In addition, if customers choose a product not in the recommendation list, the proposed models can also compute the bundle price by combining the chosen product with the items already in the shopping cart. 7 Concluding Remarks This paper provides an innovative approach to promote customer spending with online etailers by providing dynamic bundle prices based on the product portfolio chosen by shoppers. Unlike prior research in this area, this paper includes product selection through ORS, coupled with a dynamic pricing model that integrates customers’ preferences, customers savings, and etailers’ profits. Furthermore, the incorporation of customers’ multi-stage purchasing behavior in the decision process and the development of the heuristic method afford our models the capability to provide real-time prices appealing to customers. The proposed dynamic bundle pricing strategy makes sure that the offered price is not dependent on the order (sequence) of purchase and customers can arrive at the same price no matter when products are added into or removed from the shopping cart. To sensibly implement the proposed model, we design a heuristic method to arrive at a near-optimal solution within a
30
very short time. We extend the bundle pricing model to incorporate budget limits and coupon offerings. The numerical study shows that the proposed model can generate more profits for etailers and more savings for customers and therefore is a win-win strategy. In terms of future research one possibility is that in actual applications e-tailers may adjust the selling price according to their inventory level. They could provide a bigger discount when the inventory level of a product is high and a smaller discount when the inventory level is low. Incorporating a product’s inventory level to the dynamic bundle pricing strategy could be a future extension to the model. Of course, such an extension would only be of value for sellers of rival goods. Sellers of non-rival goods, e.g. information goods like software, videos, news reports, stock prices, etc. would not have an inventory that would be subject to this type of constraint. Therefore, the current model handles such non-rival cases. In recent years we have seen a burst of activities in online retailing. As is typical in the adoption of information technology, the initial applications have tended to model the virtual world implementations directly after their real world analogs. As e-commerce progresses we can expect to see advances in taking advantage of the unique characteristics of the online environment, in particular, the opportunity to dynamically price goods in ways that benefit both suppliers and buyers. References 1. Ansari, A.; Essegaier, S.; and Kohli, R. Internet recommendation systems, Journal of Marketing Research, 37, 3 (2000), 363-375. 2. Bakos, Y., and Brynjolfsson, E. Bundling information goods: Pricing, profits, and efficiency, Management Science, 45, 12 (1999), 1613-1630. 3. Bapna, R.; Goes, P.; and Gupta, A. Auctioning vertically integrated online services: Computational approaches for real-time allocation, Journal of Management Information Systems, 25, 3 (2008), 65-97. 4. Chen, L.S.; Hsu, F.H.; Chen, M.C.; and Hsu, Y.C. Developing recommender systems with the consideration of product profitability for sellers, Information Sciences, 178, 4 (2008), 10321048. 31
5. Elmaghraby, W., and Keskinocak, P. Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions, Management Science, 49, 10 (2003), 1287-1305. 6. Fan, M.; Kumar, S.; and Whinston, A. Selling or advertising: Strategies for providing digital media online, Journal of Management Information Systems, 24, 3 (2008), 143-166. 7. Garfinkel, R.; Gopal, R.; Pathak, B.; and Yin, F. Shopbot 2.0: Integrating recommendations and promotions with comparison shopping, Decision Support Systems, 46, 1 (2008), 61-69. 8. Geng, X.; Stinchcombe, M.B.; and Whinston, A.B. Bundling information goods of decreasing value, Management Science, 51, 4 (2005), 662-667. 9. Gopal, R.D.; Phatak, B.; Tripathi, A.; and Yin, F. From fatwallet to ebay: An investigation of online deal forums and sales promotions, Journal of Retailing, 82, 2 (2006), 155-164. 10. Häubl, G., and Trifts, V. Consumer decision making in online shopping environments: The effects of interactive decision aids, Marketing Science, 19, 1 (2000), 4. 11. Heller, M. Is dynamic pricing really so bad?, CIO Magazine, (2000). 12. Hitt, L.M., and Chen, P.Y. Bundling with customer self-selection: A simple approach to bundling low-marginal-cost goods, Management Science, 51, 10 (2005), 1481-1493. 13. Hui, W.; Byungjoon, Y.O.O.; and Kar Yan, T.A.M. The optimal number of versions: Why does goldilocks pricing work for information goods?, Journal of Management Information Systems, 24, 3 (2007), 167-191. 14. Internetretailer.com. Online retail sales to grow 11% this year to $156 billion, Forrester says. February 2, 2009, www.Internetretailer.com/dailyNews.asp?id=29287. 15. Kannan, P.K., and Praveen, K.K. Dynamic pricing on the Internet: Importance and implications for consumer behavior, International Journal of Electronic Commerce, 5, 3 (2001), 63-83. 16. Kauffman, R.J., and Wang, B. New buyers' arrival under dynamic pricing market microstructure: The case of group-buying discounts on the Internet Journal of Management Information Systems, 18, 2 (2001), 157-188. 17. Khouja, M., and Park, S. Optimal pricing of digital experience goods under piracy, Journal of Management Information Systems, 24, 3 (2007), 109-141. 18. Kocas, C. Evolution of prices in electronic markets under diffusion of price-comparison shopping, Journal of Management Information Systems, 19, 3 (2002), 99-119. 19. Kohli, R.; Devaraj, S.; and Mahmood, A. Understanding determinants of online consumer satisfaction: A decision process perspective, Journal of Management Information Systems, 21, 1 (2004), 115-135. 20. Liang, T.P.; Lai, H.J.; and Ku, Y.C. Personalized content recommendation and user satisfaction: Theoretical synthesis and empirical findings, Journal of Management Information Systems, 23, 3 (2007), 45-70. 21. Linden, G.; Smith, B.; and York, J. Amazon.com recommendations: item-to-item collaborative filtering, IEEE Internet Computing, 7, 1 (2003), 76-80. 22. McCardle, K. F.; Rajaram, K.; and Tang, C. S. Bundling retail products: Models and analysis, European Journal of Operational Research, 177, 2 (2007), 1197-1217. 23. Narasimhan, C. A price discrimination theory of coupons, Marketing Science, 3, 2 (1984), 128-147. 24. Netessine, S.; Savin, S.; and Xiao, W.Q. Revenue management through dynamic crossselling in e-commerce retailing, Operations Research, 54, 5 (2006), 893-913. 25. Qiu, L., and Benbasat, I. Evaluating anthropomorphic product recommendation agents: A
32
social relationship perspective to designing information systems, Journal of Management Information Systems 25, 4 (2009), 145-182. 26. Ramnath, K.C., and Kumar, K.R. Examining the role of" free" product-augmenting online services in pricing and customer retention strategies, Journal of Management Information Systems, 22, 1 (2005), 355-377. 27. Internetretailer.com. Internet retailer's top 500 guide (2008 Edition): Vertical Web Media, 2008. 28. Robert, G.; Ram, G.; Bhavik, P.; and Fang, Y. Shopbot 2.0: Integrating recommendations and promotions with comparison shopping, Decision Support Systems, 46, 1 (2008), 61-69. 29. Sahay, A. How to reap higher profits with dynamic pricing, MIT Sloan management review, 48, 4 (2008), 53-60. 30. Bohte, S.M., Gerding, E.H. and Poutre, H.L. Market-based recommendation: Agents that compete for consumer attention, ACM Transactions on Internet Technology, 4, 4 (2004), 420-448. 31. Ulkumen, G.; Thomas, M.; and Morwitz, V. Will I spend more in 12 months or a year? The effect of ease of estimation and confidence on budget estimates, Journal of Consumer Research, 35, 2 (2008), 245-256. 32. Venkatesh, R., and Kamakura, W. Optimal Bundling and Pricing under a Monopoly: Contrasting Complements and Substitutes from Independently Valued Products, The Journal of Business, 76, 2 (2003), 211-231. 33. Venkatesh, R., and Mahajan, V. A probabilistic approach to pricing a bundle of products or services, Journal of Marketing Research, 30, 4 (1993), 494-508. 34. Wang, T.; Venkatesh, R.; and Chatterjee, R. Reservation price as a range: An incentivecompatible measurement approach, Journal of Marketing Research, 44, 2 (2007), 200-213. 35. Wang, W., and Benbasat, I. Recommendation agents for electronic commerce: Effects of explanation facilities on trusting beliefs, Journal of Management Information Systems, 23, 4 (2007), 217-246. 36. Wu, S.Y.; Hitt, L.M.; Chen, P.Y.; and Anandalingam, G. Customized bundle pricing for information goods: A nonlinear mixed-Integer programming approach, Management Science, 54, 3 (2008), 608–622. 37. Yu, J.S.; Gonzalez-Zugasti, J.P.; and Otto, K.N. Product architecture definition based upon customer demands, Journal of Mechanical Design, 121, 3 (1999), 329-335.
Figure 1a. Pricing Example from Amazon.com
33
Figure 1b. Pricing Example from Amazon.com
1 Calculate the lower bound lowBound of p according to constraint (7). I
lowBound =
c i 1
S i
c Rj .
2 Calculate the upper bound upBound of p according to constraints (5), and (6). For i =1 to I Calculate the bundle price p-i of the products {gS1 , …, gSi-1, gSi+1, …, gSI, gRj }. End For S S R upBound = min{{ pi pi , i 1,..., I } { p p j }} . 3 Search the optimal price with the following fixed step length method Set the step length stepLen in the search of optimal price to a constant integer. Initialize the intermediate variable of optimal price: altPrice = upBound. Initialize the maximum profit and intermediate variable of profit: maxProfit = altProfit = 0. While altPrice >= lowBound, Do Count the number NC of customers whose reservation prices for the bundle are larger than altPrice. Calculate the intermediate variable of maximum profit: altProfit = NC(altPrice – cost). Real number cost is the cost of the bundle. If altProfit is larger than maxProfit p = altPrice; maxProfit = altProfit. End If altPrice = altPrice – (upBound – lowBound)/stepLen
End While Figure 2. Quasi-optimal Method for the Proposed Model
34
The heuristic method to calculate the bundle price p-i: Calculate the lower bound of p-i: i 1
lowBoundP-i =
c u 1
S u
I
c
u i 1
S u
c Rj .
Calculate the upper bound of p-i as follows: Find the product gSv from {gS1 , …, gSi-1, gSi+1, …, gSI, gRj } that has the lowest price. Calculate the upper bound of p-v as follows: upBoundP-i = p-v + pv. where p-v is the optimal price for the product bundle: {gS1 , …, gSi-1, gSi+1, …, gSI, gRj } – { gSv }, which is also calculated by the heuristic method. Search the optimal price of p-i in [lowBoundP-i, upBoundP-i] with the fixed step length method. Figure 3. The Heuristic Method to Calculate p-i
Shopping cart B
Recommendation
A
B
C
Reservation price
0.8
3
2.5
Posted price
1
2
3
Recommendation (when B in the cart)
Reservation price
Shopping cart
B, A
Shopping cart
B, A, F
Shopping cart
A 0.8
C
D
2.5
4.3
Posted price
1
3
4
Marginal price
0.7
2.8
3.9
Recommendation (when B and A in the cart)
C
F
G
Reservation price
2.5
5.5
7.3
Posted price
3
6
7
Marginal price
2.7
5.3
6.8
Recommendation (when B, A, F in the cart)
D
E
H
Reservation price
4.3
4.8
7.5
Posted price
4
5
8
Marginal price
3.8
4.6
7.7
B, F Calculate bundle price of products B and F Recommendation
Check out
(when B and F in the cart)
C
E
H
Reservation price
2.5
4.8
7.5
Posted price
3
5
8
Marginal price
2.6
4.7
7.5
Figure 4. Illustration of the proposed ODBP model 35
Figure 5. The Probability Density Functions of U(u–b, u+b) (u = 3.528) No maxProfit altPrice coupon
Yes maxProfit = altProfit p = altPrice coupon = (0,0)
altProfit >= maxProfit
Is any coupon activated by altPrice
Yes
Find the activated coupon (ok, dk)
No
altPrice = altPrice – (upBound – lowBound)/stepLen
maxProfit = profitCoupon Yes p = altPrice coupon = (ok, dk)
profitCoupon >=maxProfit
Calculate the profits Yes profitCoupon derived from (altPrice – dk)
No No
Figure 6. Decision logic flow
36
altPrice - dk>= lowBound
Figure 7. Customers’ Expenditures in ODBP_BC and ODBP_B Models
Figure 8. E-tailer’s Profits in ODBP_BC and ODBP_B Models
37
Table 1. Definition of Parameters Given parameters The total number of potential customers of the e-tailer. M The total number of products for sale online. N The number of products in the shopping cart. I The number of products in the recommendation list. J S The products in the shopping cart, i = 1, 2, …, I. gi The bundle price of all products in the shopping cart. pS The posted price of product gSi. pSi S The cost of product gSi. ci S r m,i Customer m’s reservation price for gSi. The products in the recommendation list, j = 1, 2, …, J. gRj The price of product gRj. pRj R The cost of product gRj. cj rRm,j Customer m’s reservation price for gRj. The budget of customer m, m = 1,…, M. bm (ok, dk) The kth kind of coupon with the trigger price ok and dollar discount dk. S S (o , d ) Coupon given to the bundle {gS1 , …, gSi, …, gSI} in the shopping cart. (o-i, d-i) Coupon received when {gS1 , …, gSi-1, gSi+1, …, gSI, gRj } are in the shopping cart. Decision variables or intermediate variables Bundle price of products {gS1 , …, gSi-1, gSi+1, …, gSI, gRj }, i = 1, 2, …, I. p-i The decision variable which is the bundle price for the bundle {gS1,…, gSi,…, gSI, gRj }. p The decision variable which is one if customer m buys the bundle {gS1,…, gSi,…, gSI, gRj }, Xm and zero otherwise. The decision variable which is one if the e-tailer choose to offer the kth kind of coupon, and Yk zero otherwise.
Table 2. E-tailer’s Profits and Customers’ Savings in the Proposed Strategy E-tailer’s profits Customers’ savings # of Profit products Unbundling Bundling improvement Unbundling Bundling Savings profit Profit payout payout (%) 2 178.7 338.6 89.5% 9.947 9.343 0.604 3 238.3 502.8 111.0% 15.220 14.142 1.078 4 303.2 696.5 129.7% 20.536 19.017 1.519 5 357.5 897.6 151.1% 25.684 23.739 1.945 6 410.7 1113.5 171.1% 30.745 28.391 2.354 7 459.8 1334.7 190.3% 35.750 33.021 2.729 8 509.7 1569.2 207.9% 40.819 37.695 3.124
38
New Customers (%) 94.0% 151.0% 203.1% 244.6% 277.1% 306.5% 336.8%
Table 3. Comparison of the Heuristic Method and Quasi-optimal Method
# of products 2 3 4 5 6 7 8
Execution time (sec.) Quasi-optimal method 0.000 0.001 0.006 0.026 0.156 1.089 8.730
Heuristic method 0.000 0.001 0.001 0.003 0.005 0.007 0.010
Efficiency improvement 0.0% 0.0% 83.3% 88.5% 96.8% 99.4% 99.9%
Optimal price Quasi-optimal method 9.963 14.374 18.690 23.192 28.664 33.770 38.664
Heuristic method 9.963 14.374 18.683 23.189 28.667 33.776 38.679
T test
Sig (2-tailed) = 0.483
Table 4. Impact of the Scale of Reservation Prices β # of products 2 3 4 5 6 7 8
E-tailer’s profit improvement
Customers’ savings
0.1
0.15
0.25
0.3
0.1
0.15
0.25
0.3
134.426 179.501 225.005 262.146 287.139 304.734 314.529
148.864 242.026 342.170 455.882 580.101 703.409 832.086
158.075 259.827 389.678 545.437 709.168 890.579 1073.111
160.173 272.371 403.494 550.696 716.151 888.751 1082.499
0.285 0.461 0.603 0.722 0.826 0.930 1.015
0.440 0.783 1.084 1.337 1.579 1.828 2.060
0.743 1.318 1.863 2.430 2.963 3.524 4.039
0.885 1.538 2.220 2.865 3.529 4.204 4.865
Table 5. Impacts of the Distribution Type of Reservation Prices β # of products 2 3 4 5 6 7 8
E-tailer’s profit improvement Normal
Uniform
149.073 223.371 314.920 431.671 554.778 687.534 829.016
151.408 240.836 360.857 489.798 635.673 795.395 960.128
Customers’ savings
0.3N&0.7U 0.7N&0.3U Normal Uniform 0.3N&0.7U 0.7N&0.3U 160.721 257.194 377.009 509.959 661.629 812.714 983.033
149.245 230.098 332.973 452.668 577.038 714.439 869.049
39
0.747 1.321 1.860 2.445 3.034 3.619 4.187
0.603 1.042 1.446 1.847 2.231 2.617 3.006
0.717 1.210 1.677 2.124 2.585 2.988 3.466
0.726 1.250 1.789 2.332 2.824 3.364 3.918
Table 6. The Impact of Customers’ Budgets on the E-tailer’s Profits Case 1 (N(20,4)) # of products 2 3 4 5 6 7 8 # of products 2 3 4 5 6 7 8
Unbundling profit 165.896 161.116 115.690 65.010 31.873 16.494 12.232
Bundling profit
Case 2 (N(30,6))
Profit improvement (%)
320.008 372.959 329.834 227.997 137.036 83.955 55.869 Case 3 (N(40,8))
Unbundling profit
92.9% 131.5% 185.1% 250.7% 329.9% 409.0% 356.8%
162.115 216.678 233.890 209.781 162.520 103.368 67.427
Bundling profit
Profit improvement (%)
311.388 465.262 582.789 600.824 541.872 411.335 292.400 Case 4 (N(50,10))
92.1% 114.7% 149.2% 186.4% 233.4% 297.9% 333.7%
Unbundling profit
Bundling profit
Profit improvement (%)
Unbundling profit
Bundling profit
Profit improvement (%)
178.021 234.513 287.714 315.659 304.633 265.459 220.961
334.713 489.786 659.130 813.856 890.115 894.495 791.111
88.0% 108.9% 129.1% 157.8% 192.2% 237.0% 258.0%
184.146 243.795 300.059 346.853 375.177 384.866 392.115
338.672 506.405 688.989 873.347 1043.267 1169.677 1212.807
83.9% 107.7% 129.6% 151.8% 178.1% 203.9% 209.3%
Table 7. The Probabilities of Receiving Coupons Probability of receiving coupon (%)
Expected savings from coupon
# of products
(0,0)
(1,15)
(3, 30)
(5, 45)
2
0.056
0.056
0.000
0.000
0.056
3
0.230
0.230
0.000
0.000
0.230
4
0.417
0.415
0.002
0.000
0.422
5
0.458
0.420
0.038
0.000
0.533
6
0.433
0.295
0.136
0.002
0.714
7
0.643
0.152
0.190
0.016
0.799
8
0.605
0.063
0.257
0.076
1.212
40
