MPIS: maximal-profit item selection with cross-selling considerations

In the literature of data mining, many different algorithms for association rule mining have been proposed. However, there is relatively little study on how association rules can aid in more specific targets. One of the applications for association rules - maximal-profit item selection with cross-selling effect (MPIS) problem - is investigated. The problem is about selecting a subset of items, which can give the maximal profit with the consideration of cross-selling. We prove that a simple version of this problem is NP-hard. We propose a new approach to the problem with the consideration of the loss rule - a kind of association rule to model the cross-selling effect. We show that the problem can be transformed to a quadratic programming problem. In case quadratic programming is not applicable, we also propose a heuristic approach. Experiments are conducted to show that both of the proposed methods are highly effective and efficient.