Design of a Bundle Shopbot. Abstract

Transcription

1 Design of a Bundle Shopbot Robert Garfinkel 1 ( robert.garfinkel@business.uconn.edu) Ram Gopal 1 ( ram@business.uconn.edu) Arvind Tripathi 2 ( tripathi@u.washington.edu) Fang Yin 1 ( fang.yin@business.uconn.edu) 1 School of Business, University of Connecticut, Storrs, Connecticut, U.S.A. 2 School of Business, University of Washington, Seattle, Washington, U.S.A. Abstract The increasing proliferation of online shopping and purchasing has naturally led to a growth in the popularity of comparison-shopping search engines, popularly known as shopbots. We extend the one-product-at-a-time search approach used in current shopbot implementations to consider purchasing plans for a bundle of items. Our approach leverages bundle-based pricing and promotional deals offered by online merchants to extract substantial savings. The problem of choosing the cheapest cost to purchase a bundle of items is modeled as a set covering problem and is shown to be NP-Hard. Interestingly, our approach can also identify freebies that consumers can obtain at no extra cost. We develop heuristic approaches that can be employed when the number of items is large or when the real-time nature of shopbot applications dictates quick response rates to consumer queries. A detailed illustration with real-world data from major retailers suggests that optimal solutions to the proposed models can result in significant savings for bundle purchasing consumers, and frequently identify freebies for consumers. The heuristic approach also performs extremely well and is thus practical for shopbot implementation.

2 Design of a Bundle Shopbot 1 Introduction The Internet has dramatically reduced buyer search costs by providing easy information retrieval (Bakos 1997). On the other hand researchers have found significant price variation on the Internet even for identical commodities such as books and CDs, to name a few (Bailey 1998; Brynjolfsson and Smith 2000). This variation and the large number of vendors have made it difficult for a user to find the best price for an item or items. In response, a number of comparison-shopping search engines, widely known as shopbots, have become popular (e.g., mysimon.com, Froogle.com, and PriceGrabber.com). At these web sites a shopper can enter the product name and specification, and the shopbot will search a large number of vendors and return the prices offered by these retailers, as well as other information such as shipping cost and availability. Recent work has addressed issues surrounding the impact of shopbots on retailer pricing strategies (Smith 2002), and operational design improvements to enhance a consumer s overall utility with the shopbots (Montgomery et al. 2004). Current shopbots are geared towards one-product-at-a-time search, and thus do not consider bundle pricing and promotions that are frequently offered by online retailers. There is a considerable literature on the benefits of bundling from the seller s side, beginning with the work of Stigler (1963) on how bundling can increase sellers profit (see also Stremersch and Tellis, 2002). Adam and Yellen (1976) classified three modes of bundling strategies, namely pure bundling, mixed bundling, and component selling (pure unbundling). In pure bundling, individual items are not offered. Mixed bundling is a combination of pure bundling and component selling. On the other hand pure bundling is not a concept of interest from the buyer s point of view since one can simply consider components to be minimal sets of goods that can be purchased individually. Since we focus on the buyer s problem we will assume that all bundling is mixed, meaning that all components are offered individually for purchase, and are also included in other bundles. The focus of our work is on the development of models for shopbots that leverage bundle pricing and promotional deals offered by online merchants to extract price savings. It is intended to operate in the presence of the demand for multiple items by a user. Note that it will generally not be the case that there exists an offered bundle that is identical to, or even includes, the set of goods demanded by the user. In the absence of such a shopbot, a shopper s 2

3 only recourse via current shopbots is to initiate the search for each product and then combine the search results on her own. In addition to its inconvenience, this one-product-at-a-time search pattern may result in loss of potential savings to the shopper since vendors generally offer promotional deals and discounts for bundles. In this research we develop models for a shopbot engine that aids consumers in procuring item bundles at the lowest possible price. The problem of choosing the cheapest cost to purchase a bundle of items is modeled as a set covering problem and is shown to be NP-Hard. Interestingly, our approach can also identify freebies that consumers can obtain at no extra cost. We develop heuristic approaches that can be employed when the number of items is large or when the real-time nature of shopbot applications dictates quick response rates to consumer queries. A detailed illustration with real-world data from major retailers suggests that optimal solutions to the proposed models can result in significant savings for bundle purchasing consumers, and frequently identify freebies for consumers. The heuristic approach also performs extremely well and is thus practical for shopbot implementation. The remainder of the paper is organized as follows. Bundle purchase models are given in Section 2. Algorithms are described in Section 3. Computational experience with real data is presented in Section 4, and conclusions follow in Section 5. 2 Bundle Purchase Models 2.1 General classifications of bundles The various general bundling strategies implemented have been implemented by retailers (Simon and Wuebker 1999) are listed below: Deterministic bundling: Exactly one set of predetermined items is included in the bundle. Non deterministic bundling: This includes, for instance, the following: Tie-in bundling: The buyer is required to buy one major product (e.g., digital camera, mp3 player) to qualify for discounted prices on other products (e.g., three software products for $48). Usually there are comprehensive lists for both the major and tied-in products. A special case is add-on bundling, where the buyer is required to buy one product (e.g., wireless router) to get a free product (e.g., wireless card). Another special case is cross promotion where the buyer is required to purchase one product to qualify for a discount on another product. However, the buyer has the option of not purchasing the additional product. 3

4 Total value discount: If the total amount of an order is above a certain threshold, the order gets an extra discount (e.g., 10% off any order above $100). 2.2 The General Model Consider a buyer with demand for one of each of a set of items S 0. There is a set of related bundles B := {B 1,B 2,...} (i.e. each bundle in B contains at least one element of S 0 ), offered by the retailers, including at least the S 0 degenerate bundles {i} for all i S 0.Eachitemi (we will often abuse notation by not distinguishing between a set and its index set) has an original (unbundled) cost given by c i > 0. The unbundled cost of a set T of items is denoted c(t ):= P c i and it represents the benchmark for price savings. Also let S j be the set of items in B j, and the set of i T all items in B is denoted by S := S S j.thecostofb j is f j > 0,sothatf j = c i if S j = {i}. LetB(i) be the set of j B bundles that contain item i. Then the problem (CB) of choosing the cheapest set of bundles that satisfies the demand for S 0 can be modeled as the following set covering problem: min X j B f j x j (1) s.t. X x j 1, i S 0 (2) j B(i) x j binary, j B (3) Note that the model CB is set covering, rather than set partitioning. That is, the constraints (2) allow the buyer to receive additional goods beyond the desired set S 0. Unless there is a negative utility associated with receiving additional goods, these constraints are preferred to replacing them with P x j =1, i S 0 (4) j B(i) which would result in a set partitioning model. That follows since set covering is a relaxation of set partitioning and thus always results in an objective value that is never worse than that of set partitioning. If B is an optimal set of bundles from CB, denote by S := S S j the corresponding optimal set of j B goods. Then, if B is purchased, the buyer may receive the set F of additional goods ( freebies ) beyond single copies of the elements of S 0.Thatis,F contains at least one copy of every element of S \S 0, as well as possible extra elements of S 0. 4

5 2.3 Complexity of the Problem Given the bundle set B, along with the vector of bundle prices, the problem of choosing an optimal subset of B is set covering, which is shown (e.g. Garey and Johnson 1979) to be NP-Hard. On the other hand (see e.g. Nemhauser and Wolsey 1988) set covering problems are among the best-solved NP-Hard problems by both exact and heuristic algorithms. Of course the complexity of CB is a function of the size of the problem in terms of the number of constraints and variables. The former is determined by the cardinality of S 0 i.e. the number of items specified by the user. The latter can be bounded by 2 S0 1, since if two bundles contain identical elements of S 0, the shopbot will simply choose the cheaper of the two. On the other hand the problem can be shown to be hard, without resorting to set covering, in the presence of total value discounts. Consider a seller who offers a total value discount of α if the buyer spends more than a floor g. That is, the price of a set T of items is ½ c(t ),ifc(t ) g (1 α)c(t ),otherwise As before let S denote the set of all items offered by the seller and let T 0 := S S 0 be those items in the bundle desired by the buyer. Any items purchased in S\T 0 have no intrinsic value except for the possible discount. If c(t 0 ) g the buyer will purchase only the items in T 0, so assume that c(t 0 ) <g.thenletx S\T 0 be the additional items purchased. To get the discount it must be true that c(x) g c(t 0 ). Itisalsoeasytoseethat X must satisfy αc(t 0 ) (1 α)c(x) or else the discount does not outweigh the additional cost of X. Then the resulting problem is s.t. X min X i S\T 0 c i y i (5) c i y i g c(t 0 ) (6) i S\T 0 X c i y i α 1 α c(t 0) (7) i S\T 0 y i 0 and integer, i S\T 0 (8) But even as α 1, so that the constraint (7) becomes inoperative, the remaining problem is a minimization 5

6 variation of the standard Integer Knapsack Problem, with the special property that the cost coefficients and the constraint coefficients are the same. That special case is known to be NP-Hard (see e.g. Martello and Toth 1990). 2.4 Generating the Bundle Set Determination of the bundle set B to be used in solving CB is clearly an important issue. Here we touch on it briefly and leave extensive analysis to follow up research. In very general terms it follows that as the set B is expanded the solutions to CB will improve. Yet, there are two downsides to making B large. In general CB becomes more difficult to solve as B increases and, in addition, there is the cost of searching the Web to find additional promotions. Finally, thesizeandstructureofb will also be determined by the particular bundle promotions as indicated in Section 2.1. For non deterministic bundling there may be multiple elements of B for a given promotion and set S 0. The shopbot may simply choose to add only one element to B in these circumstances but, as shown in the previous subsection, choosing the cheapest such element, for at least one type of promotion, is itself an NP-Hard problem. Thus it may be useful to develop heuristic rules for the generation of B. 3 Algorithms for CB For consumer purchases that involve only a few items, the exact solution of CB can easily be found by generic integer programming packages or by specialized set covering algorithms. However, a heuristic approach may be useful in the following cases: (a) in commercial purchases for which S 0 could be quite large, and (b) when there are potential benefits to shaving off valuable seconds in responding to consumer requests. Our computational experiments with real-world data suggest that the time savings are in the order of 98 to 99 percent when heuristic approaches are used. A Standard Greedy Heuristic A standard greedy heuristic for set covering is given in Nemhauser and Wolsey (1988). In words it is to do the following. At each step choose that bundle that minimizes the ratio of the cost of the bundle to the number of desired items in the bundle that have not been selected at previous steps. Thus, at each step you will add at least one more desired item to the bundle. The heuristic has order O( B S 0 ) and is formalized below: Initialize: M 1 = S 0, N 1 = B, t =1, While M t 6=φ do, Select j t N t to min{f j / S j M t }, 6

7 End while Let N t+1 = N t \{j t }, M t+1 = M t \{S j t},andt = t +1, The solution is x j =1for j/ N t+1 and x j =0otherwise. We can observe that this standard greedy heuristic is not able to take advantage of the fact that, in our application, there always exist degenerate bundles for every element of S 0 and that the costs of these bundles may be taken into account. Thus a natural modification of that heuristic is to replace the step Select j t N t to min{f j / S j M t }, with Select j t N t P to min{f j / c i }. i S j M t That is, at each step choose the bundle that minimizes the ratio of the cost of the bundle to the retail value of the desired items in the bundle that have not been selected at previous steps. It will be seen in the computational results of the next section that, for this application, the modified heuristic gives superior results. Finally it should be noted that the solution may yield redundant bundles, namely any bundle that is not uniquely responsible for supplying at least one desired item. Upon termination of the heuristic, any such bundles can be discarded, one-at-a-time, yielding a lower cost solution. 4 Detailed Illustration To ascertain the potential practical benefits from deploying our models, we conducted a detailed analysis with real-world data on computer-related products. Recent reports indicate that this product category which includes software, wireless gadgets, printers, memories, and digital cameras is one of the most commonly purchased categories online (shop.org 2004). To limit any confounding retailer brand effects that may influence a shopper (Smith and Brynjolfsson 2001), we carefully selected the set of retailers for consideration. We initially started with Best Buy, and then identified its main competitors in the category of computer products. This information was derived from Hoovers ( which provides in-depth information on 40,000 of the world s top business entities as well as comprehensive industry and market information. This process led to the selection of the following 14 retailers: Best Buy,CircuitCity,BUY.com,CDW.com,Staples,Kmart,Wal-Mart,OfficeMax, Office Depot, Sears, Gateway, Radio Shack, CompUSA, Amazon.com. 7

8 We then monitored these retailers for a period of 10 days in early 2004, and captured their bundle-based pricing and promotional offers for computer-related products. From this we selected a total of 194 bundle offerings involving 36 products. Table 1 lists summary statistics on the individual items and the bundles. We evaluated the bundle shopping models by varying the size of the bundle from 2 to 20. For each bundle size, we randomly generated the products in the bundle from the 7 product groups. One thousand bundles for each bundle size were generated, resulting in a total of simulation runs. Items Bundles mean $ mean $ max $ max $ min $ min $ 0.01 std dev $ std dev $ n 36 n 194 Table 1 Summary Statistics of the Sample Distribution of Savings Savings 80% 70% 60% 50% 40% 30% 20% 10% 0% 76% 19% 5% 7% 9% 11% 13% 15% 0% 2% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Percentile Figure 1 Distribution of Savings (CB) 8

9 Avg Optimal Modified Heuristic Nbr of Benchmark Avg Value % of Avg Value % of Items value of Avg Avg # of Avg # of Avg Cost Std Dev of extra Benchmark Avg Cost Avg Saving Std Dev of extra Benchmark Needed needed Saving extra items extra items items Cost items Cost items* 2 $ $ % 16.5% 0.3 $ % $ % 16.5% 0.3 $ % 3 $ $ % 11.8% 0.4 $ % $ % 11.8% 0.4 $ % 4 $ $ % 9.6% 0.5 $ % $ % 9.6% 0.5 $ % 5 $ $ % 8.3% 0.6 $ % $ % 8.3% 0.7 $ % 6 $ $ % 7.1% 0.7 $ % $ % 7.1% 0.7 $ % 7 $ $ % 7% 0.8 $ % $ % 7% 0.8 $ % 8 $ $ % 7.1% 1.0 $ % $ % 7.1% 1.0 $ % 9 $ $ % 6.8% 1.1 $ % $ % 6.8% 1.1 $ % 10 $ $ % 6.1% 1.1 $ % $ % 6.1% 1.1 $ % 11 $ $ % 5.9% 1.3 $ % $ % 5.9% 1.3 $ % 12 $ 1, $ % 5.5% 1.3 $ % $ % 5.6% 1.4 $ % 13 $ 1, $ % 5.2% 1.4 $ % $ % 5.2% 1.5 $ % 14 $ 1, $ 1, % 4.9% 1.5 $ % $ 1, % 4.9% 1.6 $ % 15 $ 1, $ 1, % 4.9% 1.5 $ % $ 1, % 4.8% 1.6 $ % 16 $ 1, $ 1, % 4.8% 1.5 $ % $ 1, % 4.7% 1.6 $ % 17 $ 1, $ 1, % 4.7% 1.6 $ % $ 1, % 4.6% 1.7 $ % 18 $ 1, $ 1, % 4.4% 1.6 $ % $ 1, % 4.2% 1.8 $ % 19 $ 1, $ 1, % 4.3% 1.7 $ % $ 1, % 4.1% 1.9 $ % 20 $ 1, $ 1, % 4.1% 1.7 $ % $ 1, % 3.8% 1.9 $ % Table 2 Summary of Simulations (CB) Nbr of Items Needed Avg Performance Modified Heuristic Std Dev Lower Bound Avg Performance Standard Heurisitc Std Dev Lower Bound 2 100% 0% 100% 99.7% 1.9% 84.4% 3 100% 0% 100% 99.5% 1.8% 85.6% 4 100% 0.3% 91.3% 99% 2.5% 79.1% 5 100% 0.5% 92% 98.8% 2.6% 81.8% 6 100% 0.6% 92.6% 98.1% 3% 87.2% % 0.6% 93.6% 97.5% 3.3% 85.1% % 0.7% 93.5% 97% 3.6% 77.9% % 0.5% 94.1% 96.7% 3.4% 75.8% % 0.6% 95% 96.3% 3.1% 79.7% % 0.6% 95.1% 95.9% 3.3% 80.2% % 0.6% 95.4% 95.6% 3% 81.4% % 0.6% 96.4% 95.3% 2.9% 80.2% % 0.6% 95.7% 94.8% 3% 81.7% % 0.7% 95.8% 94.4% 2.9% 81.2% % 0.7% 94.9% 94.4% 3% 82.1% % 0.9% 94.9% 94% 2.8% 84.5% % 0.8% 95% 93.8% 2.9% 80.8% % 1% 94.9% 93.7% 2.6% 86.4% % 1.1% 95.2% 93.6% 2.5% 86.8% All differences are significant at p <.0001 Table 3 Comparisons between the Two Heuristics Figure 1 highlights the cumulative percentage savings over the benchmark (sum of the individually-cheapest prices of items in the bundle). Positive savings were observed in over 85% of the cases. The median savings rate was 10%, and in nearly 10% of the cases the percentage savings were over 20%. Table 2 lists the complete performance of the exact algorithm and the modified heuristic for various bundle sizes. As expected, the savings increase as 9

10 the number of items in the bundle increase. The heuristic performs extremely well. Both the optimal and heuristic algorithms were able to frequently identify freebies, with more freebies identified for larger bundles. Assuming that the baseline value of a freebie is its lowest individual price, the net savings with the freebies included are 4% to 10% higher than without freebies taken into consideration. Interestingly, the heuristic procedure, in a number of instances, was able to identify slightly higher-valued freebies than the optimal algorithm. A performance comparison of the standard heuristic for set covering with our modified heuristic is shown in Table 3. The performance is measured by the ratio of optimal objective value from exact algorithm over objective value from the heuristic. The modified heuristic significantly outperformed the standard heuristic for all bundle sizes. 5 Concluding Remarks We have provided a model for computing an optimal purchase plan to procure a bundle of items from competing sellers who offer bundle-based prices and promotions. Detailed analysis of the models with real-world data on computer-related products from major retailers reveals significant savings for bundle purchases and frequent opportunities to obtain freebies. These findings point to the viability of the proposed models for implementation consideration in current shopbot systems. Our work can be extended in a number of ways. Our finding that the savings increase with the number of items in the bundle suggests potential benefits to aggregating various consumer purchase plans. Consideration of retailer reputation and substitutable products is also worthy of further study. Finally, while mechanisms to automate retrieval of individual item prices from a retailer exist and are in use by current shopbots, no such mechanisms exist to automate the procurement of bundle prices and promotions. While the wide variety of bundling and bundle promotion strategies used by online retailers pose significant challenges, this can contribute immensely to the popularity and usage of shopbots. References Adams, W. J., J. L. Yellen Commodity Bundling and the Burden of Monopoly. Q. J. Econ. 90(3) Bailey, J Electronic Commerce: Prices and Consumer Issues for Three Products: Books, Compact Discs, and Software. Organisation for Economic Co-Operation and Development 98(4). 10

11 Bakos, Y. J Reducing Buyer Search Costs: Implication for Electronic Marketplaces. Manage. Sci. 43(12) Brynjolfsson, E., M. D. Smith Frictionless Commerce? A Comparison of Internet and Conventional Retailers. Manage. Sci. 46(4) Garey, M. R., D.S. Johnson Computers and Intractability. Freeman. Martello, S. and P. Toth Knapsack problems: algorithms and computer implementations. John Wiley & Sons, New York. Montgomery, A. L., K. Hosanagar, R. Krishnan, K. B. Clay Designing a Better Shopbot. Manage. Sci. 50(2) Nemhauser, G.L., L. A. Wolsey Integer and Combinatorial Optimization. John Wiley & Sons, New York. Shop.Org Online Sales Skyrocket as Profitability Jumps, According to Shop.Org/Forrester Research Study. accessed on May 25, Simon, H., G. Wuebker Bundling - a Powerful Method to Better Exploit Profit Potential. In R. Fuerderer, A. Herrmann and G. Wuebker (Ed.), Optimal Bundling: Marketing Strategies for Improving Economic Performance. Springer-Verlag, Berlin Smith, M. D The Impact of Shopbots on Electronic Markets. J. Acad. Market. Sci. 30(4) Smith, M. D., E. Brynjolfsson Consumer Decision Making at an Internet Shopbot: Brand Still Matters. J. Ind. Econ. 49(4) Stigler, G. J United States Vs. Loew s Inc.: A Note on Block Booking. Supreme Court Rev Stremersch, S., G. J. Tellis Strategic Bundling of Products and Prices: A New Synthesis for Marketing. J. Marketing 66(1)