Hierarchical Choice Models and Properties of Optimal and Competitive Assortments

This paper studies centralized and decentralized assortment planning problems for a product category with heterogenous product types from two brands. We model consumer choices in such a product category by two hierarchical choice models: a brand-primary choice model in which consumers choose a brand …rst, then a product type in the chosen brand, and a type-primary choice model in which consumers choose a product type …rst, then a brand within that product type. We …nd that the optimal assortments under centralized management and the competitive assortments under decentralized management have similar properties within the same consumer choice model, but have quite distinctive properties across di¤erent consumer choice models. Speci…cally, with the brand-primary choice model, both the optimal and the competitive assortments for each brand consist of the most popular product types from the brand. With the type-primary choice model, the optimal and the competitive assortments for each brand may not always consist of the most popular product types of the brand. However, the product types that are o¤ered by at least one brand consist of a set of the most popular product types. In addition, the product types that are o¤ered by both brands also consist of a (possibly smaller) set of the most popular product types. These properties of the optimal and the competitive assortments can be used as e¤ective guidelines for managers to identify the best assortments, and to rule out non-optimal assortments. Our results imply that, in order to be able to o¤er the right set of products, category and/or brand managers should pay close attention to identify what hierarchical process consumers commonly follow to make purchase decisions in product categories they manage.