Product selection problem: improve market share by learning consumer behavior

It is often crucial for manufacturers to decide what products to produce so that they can increase their market share in an increasingly fierce market. To decide which products to produce, manufacturers need to analyze the consumers' requirements and how consumers make their purchase decisions so that the new products will be competitive in the market. In this paper, we first present a general distance-based product adoption model to capture consumers' purchase behavior. Using this model, various distance metrics can be used to describe different real life purchase behavior. We then provide a learning algorithm to decide which set of distance metrics one should use when we are given some historical purchase data. Based on the product adoption model, we formalize the k most marketable products (or k-MMP) selection problem and formally prove that the problem is NP-hard. To tackle this problem, we propose an efficient greedy-based approximation algorithm with a provable solution guarantee. Using submodularity analysis, we prove that our approximation algorithm can achieve at least 63% of the optimal solution. We apply our algorithm on both synthetic datasets and real-world datasets (TripAdvisor.com), and show that our algorithm can easily achieve five or more orders of speedup over the exhaustive search and achieve about 96% of the optimal solution on average. Our experiments also show the significant impact of different distance metrics on the results, and how proper distance metrics can improve the accuracy of product selection.