【正文】
ally do not purchase many items during a single shopping visit. Therefore, the profit margin generated per frequent purchase bination (X) could accurately be approximated by adding the profit 外文翻譯 4 margins of the market baskets (Tj) containing the same set of items, . X = Tj. However, for supermarket data, the existing formulation of the PROFSET model poses significant problems since the size of market baskets typically exceeds the size of frequent item sets. Indeed, in supermarket data, frequent item sets mostly do not contain more than 7 different products, whereas the size of the average market basket is typically 10 to 15. As a result, the existing profit allocation heuristic cannot be used anymore since it would cause the model to heavily underestimate the profit potential from crossselling effects between products. However, getting rid of this heuristic is not trivial and it will be discussed in detail in Section . A second limitation of the existing PROFSET model relates to principles of category management. Indeed, there is an increasing trend in retailing to manage product categories as separate strategic business units [6]. In other words, because of the trend to offer more products, retailers can no longer evaluate and manage each product individually. Instead, they define product categories and define marketing actions (such as promotions or store layout) on the level of these categories. The generalized PROFSET model takes this domain knowledge into account and therefore offers the retailer the ability to specify product categories and place restrictions on them. 3 The Generalized PROFSET Model In this section, we will highlight the improvements being made to the previous PROFSET model [3]. Profit Allocation Avoiding the equality constraint X = Tj results in different possible profit allocation systems. Indeed, it is important to recognize that the margin of transaction Tj can potentially be allocated to different frequent subsets of that transaction. In other words, how should the margin m (Tj) be allocated to one or more different frequent 外文翻譯 5 subsets of Tj? The idea here is that we would like to know the purchase intentions of the customer who bought Tj . Unfortunately, since the customer has already left the store, we do not possess this information. However, if we can assume that some items occur more frequently together than others because they are considered plementary by customers, then frequent item sets may be interpreted as purchase intentions of customers. Consequently, there is the additional problem of finding out which and how many purchase intentions are represented in a particular transaction Tj . Indeed, a transaction may contain several frequent subsets of different sizes, so it is not straightforward to determine which frequent sets represent the underlying purchase intentions of the customer at the time of shopping. Before proposing a solution to this problem, we will first define the concept of a maximal frequent subset of a transaction. Definition 1. Let F be the collection of all frequent subsets of a sales transaction Tj . Then YX? is called maximal, denoted as X max , if and only if. FY?? : YX? . Using this definition, we will adopt the following rationale to allocate the margin m(Tj) of a sales transaction Tj . If there exists a frequent set X = Tj, then we allocate m(Tj) to M(X), just as in the previous PROFSET model. However, if there is no such frequent set, then one maximal frequent subset X will be drawn from all maximal frequent su