Recommender systems (RSs) enhance e-commerce sales by recommending relevant products to their customers. RSs aim at implementing the firm's web-based marketing strategy to increase revenues. Generating bundles is an example of a marketing strategy that aims to satisfy consumer needs and preferences, and at the same time, to increase customers' buying scope and the firm's income. Thus, finding and recommending an optimal and personal bundle becomes very important. In this paper we introduce a novel model of bundle recommendations that integrates collaborative filtering (CF) techniques, personalized demand functions, and price modeling. This model provides a recommendation list by finding pairs of products that maximizes both, the probability of their purchase by the user and the revenue received by selling this bundles. Bundling refers to the practice of selling two or more items together as a package at a price that is below the sum of the independent prices. Optimal bundling would combine items into bundles that best fit the retailer's needs and the user's preferences, and maximize product compliance within the bundle. Thus, a single price < + is set for the two products (A, B) if purchased
jointly. One challenge is to suggest a price for a bundle that fits both the customer reservation price i.e., the maximal price buyers are accepted to pay, and the retailer’s revenue [1]. Very few studies have combined bundling strategy with recommender systems (RSs). The field of frequent item set mining and association rules deals with finding a basket of items that are frequently bought together [2]. However, these techniques are not personalized, thus not applicable for RSs. The recommendation of bundles were presented as a tailored solution for the tourism domain using casebased reasoning where case models representing the travel plan bundle were matched against the user profile and preferences [3]. The authors of [4] presented a bundle optimization using a genetic algorithm to maximize the compatibility of the products within a bundle.
However, these studies did not measure the recommendation aspect, i.e., if it is at all feasible and beneficial to predict bundle purchasing. The study presented in [5] introduces a held by the 1+ ,
1
1 +
1
,
bundle recommendation problem, in which its solution is a set of
items that maximizes some total expected reward. However, the
price aspect was not considered in the model. Our paper maximizes
the expected revenue by considering the item-to-item
cross
dependencies, user-item collaborative filtering techniques and the
demand-price function—resulting in recommendation of the best
bundle and price proposal to the user.
2. BUNDLE RECOMMENDATION MODEL
We maximize the following retailer expected revenue function:
(
) is the probability that user i will purchase the bundle, which is composed of products A and , at price T. The
A is the retailer’s cost for product A and is the retailer’s cost for product B. The proposed bundle and the price T for user i is set to maximize the expected revenue: (, , ) ∙ ( − − ) (2) (, , ) = ∀,, (, , ) In order to find (, ,
) we find the corresponding prices of
product and of product aggregated to the bundle price :
(
combinatorial principle: (6) ( ∩ mathematics, the
inclusion–exclusion ) = ( ) + ( ) − ( ∪ Using equations (5) + (6): (7) ( ∩ ) = Using Bayes’ law and equation (7):
(8) (( ∩ ) ∩ ( ∩ )) = ( ) ∙ ( | ) + () ∙ ( |) () 2.1 We assume that the Jaccard measure, , , which denotes the products' compatibility, is not affected by the price. The ( ), probabilities are found using the
CF technique; ( | ), ( |) is found by the upcoming personal demand.
Personalized Demand Graph We would like to assume that each customer has its own demand graph for each product based on his/her preferences. Thus, we developed heuristics for estimating the “personalized” demand graph for user i and item j using very sparse data. Figure 1 demonstrates the demand of a generic customer versus an enthusiastic one (i.e., one that would pay high prices) as well as an indifferent one. We assume that the difference between the demand graphs can be reflected by the following: (9) ( | ) = ( ∙, ( ) × , , 100%) where ∙, ( A) is the generic demand graph for item given that the price A and , is the personalized bias factor for user i and item . In order to find the personal bias factor, , , we scan each customer's previous purchases or his/her highest bid on an item. We compare his/her price to the median of the generic graph. For example if customer i purchased item for price A* then his/her bias factor is estimated as: (10) , = ∙, 0(.5A∗). For example (Figure 1), assume that a customer purchased the item for A*=1300; according to the generic graph, this price would be considered only by 35% of the interested population. Thus the personalized bias for this user is calculated as: , = 00.3.55 = 1.42. We can create a bias matrix for all purchases of items by users. The bias factor of products that have not been purchased by the customer can be predicted using the SVD method. Given the complete matrix, we can infer the personalized demand graph of each user i and item from the generic demand graph calculated for item and multiply it by the predicted alpha.
Our model was evaluated based on two datasets. (Dataset 1)
consists of transactions from a shopping website that sells
electronics and furniture. (Dataset 2) is a supermarket dataset from
Kaggle
(https://www.kaggle.com/c/acquire-valued-shopperschallenge). We used offline evaluation and compared our model to
SVD and CF as baseline models. We evaluated: (i) The personal
demand function by using a validation set in order to test the
predicted alphas compared to the actual alphas, using the RMSE
measure, and comparing the personal demand graph probability to
0.5 (median probability) of all purchased products in the test
setusing the RMSE measure too; (ii) The product bundling
recommendation by comparing the top 5 bundles to the top 5 items
recommended by CF and SVD algorithms. For this we used
precision, recall, the average quantity that was recommended and
purchased, and the average price paid for the recommended and
purchased products; (iii) The price bundling recommendation by
comparing the recommended price to the actual price the user paid
in the test set, measuring the sum of the absolute difference. The
recommended price was compared to the mean price of the product.
We also compared two strategies: (
ACM SIGMOD, volume 22,2 of SIGMOD Record, 207–216.