Contextual Preference Choice Model and Learning for Multi-Product Inventory Systems

Abstract

Making stocking decisions for multiple products is a complex problem that requires optimizing inventory levels while considering substitution effects. The absence of knowledge regarding demand distributions and choice structure further exacerbates the problem. Instead, we can only rely on the historical transaction data involving product feature information. In this paper, we propose a novel data-driven approach that combines a rank-based choice model with product attributes to prescribe inventory levels for multiple products. We innovate a preference learning method based on a crafted kernel regression, which adapts to the complex choice structures inherent in multi-product systems for estimating customer choices. Additionally, we utilize the Markovian property of customer choices to link individual choice behavior with aggregated inventory ordering decisions, enabling prescriptive optimization through recursion algorithms. Using the theories of large deviation and partitioning estimates in statistical learning, we establish the universal consistency results for the preference learning algorithm and demonstrate its convergence rate. Leveraging these consistent estimates, we demonstrate the asymptotic optimality of our data-driven solution method. Moreover, we employ approximation strategies to address the high dimensionality issue. Finally, we evaluate our proposed solution framework using both synthetic and real data, and the results demonstrate its promising efficacy.

Keywords: multi-product, inventory system, choice model, substitution, preference learning