A Learning and Optimization Framework for Personalized Product Design

Abstract

The problem of product design aims to select a combination of features for a new product that maximizes the revenue from selling it. We propose a learning and optimization framework for personalizing product design to customers. Our method works with choice-based conjoint datasets, commonly used in traditional conjoint experiments and advanced data collection on digital platforms. We provide finite sample performance guarantees for this framework, which fills a gap in the single product design literature by providing the first statistical learning performance guarantee. It also reveals a missing angle in the literature by examining the impact of assortment size on the convergence speed of a learning method used in choice-based conjoint analysis. Interestingly, unlike the sample size in classic statistical analysis, the assortment size has a convex effect on the convergence rate. Furthermore, we investigate the optimal assortment size for different levels of product design attractiveness through theoretical analysis, providing practical insights for collecting conjoint data more efficiently. From the optimization perspective, we show that this personalized product design problem is NP-hard and provide solution methods, including a fully polynomial-time approximation scheme under certain assumptions and an exact algorithm for the general case. We validate our theoretical findings with numerical experiments and demonstrate the efficiency of our method with case studies based on a COVID-19 vaccine dataset from a large-scale survey and a hotel room dataset from a multinational hotel chain company.

Keywords: Product Design, Conjoint Analysis, Personalization, Statistical Learning