A Partially Ranked Choice Model for Large-Scale Data-Driven Assortment Optimization

The assortment of products carried by a store has a crucial impact on its success. However, finding the right mix of products to attract a large portion of the customers is a challenging task. Several mathematical models have been proposed to optimize assortments. Most of them are based on discrete choice models that represent the buying behavior of the customers. Among them, rank-based choice models have been acknowledged for representing well high-dimensional product substitution effects and, therefore, reflect customer preferences in a reasonably realistic manner. In this work, we extend the concept of (strictly) fully ranked choice models to models with partial ranking that additionally allow for indifference among subsets of products, that is, on which the customer does not have a strict preference. We show that partially ranked choice models are theoretically equivalent to fully ranked choice models. We then propose an embedded column-generation procedure to efficiently estimate partially ranked choice models from historical transaction and assortment data. The subproblems involved can be efficiently solved by using a growing preference tree that represents partially ranked preferences, enabling us to learn preferences and optimize assortments for thousands of products. Computational experiments on artificially generated data and a case study on real industrial retail data suggest that our proposed methods outperform existing algorithms in terms of scalability, prediction accuracy, and quality of the obtained assortments.