This paper studies assortment planning and pricing for a product category with heterogenous product types from two brands. We model consumer choices by two hierarchical choice models with the Nested Multinomial Logit framework: a brand-primary model in which consumers choose a brand first, then a product type in the chosen brand, and a type-primary model in which consumers choose a product type first, then a brand within that product type. We consider a centralized regime that finds the optimal solution for the whole category and a decentralized regime that finds a competitive equilibrium between two brands. The brand competition can also be interpreted as the competition between independent retailers. We .nd that optimal and competitive assortments and prices have quite distinctive properties across different models. Specifically, with the brand-primary 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. Instead, both the product types that are offered by at least one brand and the product types that are offered by both brands consist of a set of the most popular product types. The price of a product under the centralized regime can be characterized by a sum of a mark-up that is constant across all products and brands, its procurement cost and its marginal operational cost, implying a lower price for more popular products. The mark-up may be different for each brand and product type under the decentralized regimes, implying a higher price for brands with a larger market share. These properties of the assortments and prices can be used as effective guidelines for managers to identify and price the best assortments, and to rule out non-optimal assortments. Our results suggest that, in order to o¤er the right set of products and prices, category and/or brand managers should create an assortment planning process that is aligned with the hierarchical choice process consumers commonly follow to make purchase decisions.
REF considered the joint assortment optimization and pricing problems with a restricted number of nests.