72 Clustering Products under Pairwise Positive and Negative Association Constraints in Retailing

Finding the item associations and corresponding rules are the main purposes of association mining algorithms. The resulting rules of positive associations can easily be applied for organizing supermarket shelves. However negative associations are rarely used in application domains due to the lack of universally accepted methods for finding concrete negative associations. Clustering is a proven method in data analysis to group similar objects while separating dissimilar ones. The idea of using both positive and negative item associations in a constrained clustering framework is proposed and implemented in this paper. The products of an apparel retailing firm are clustered based on their weekly sales figures in addition to the constraints originating from pair-wise positive and negative product associations. A minimum cluster size constraint is also introduced for ensuring the practicality of the clustering results in terms of generating multi-product groups to run markdown optimization algorithms on such product groups in the later stages of our overall revenue management research project in which forecasting of product sales can be conducted within each cluster in a multivariate way.