Optimal and Competitive Assortments with Endogenous Pricing Under Hierarchical Consumer Choice Models

Abstract

This paper studies assortment planning and pricing for a product category with heterogeneous product types from two brands. We model consumer choice using the nested multinomial logit framework with two different hierarchical structures: 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. We find 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, the overall assortment in the category consists of a set of most popular product types. The price of a product under the centralized regime can be characterized by a sum of a markup 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 markup may be different for each brand and product type under the decentralized regime, 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 nonoptimal assortments. Our results suggest that to offer 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 purchasing decisions. This paper was accepted by Pradeep Chintagunta and Preyas Desai, special issue editors. This paper was accepted by Pradeep Chintagunta and Preyas Desai, special issue editors.assortment planning, product variety, category management, pricing, inventory costs, nested multinomial logit model

Review on Assortment Problems in Retailing Supply Chain Management

“…It includes required and optional components and the demand of components is complementary: the change of assortment or price for one component may lead to a different demand for another component. Compared with papers above, Kök and Xu (2011) assume two types of consumer choice model (brand-primary and type-primary) and find that optimal assortment is very different under two customer choice models [14]. In each customer choice model, they formulate different assortment optimization models combined with newsvendor and EOQ inventory model.…”

Assortment Planning: Review of Literature and Industry Practice

“…Li (2007) extend the van Ryzin and Mahajan (1999) and show that under continuous traffic, the optimal assortment consists of a set of products with the highest profit rates, even when product margins are unequal. Kök and Xu (2011) use a nested logit model to study assortment decisions for a product category with heterogeneous product types from two brands. They consider two different hierarchical structures for the nests: a brand-primary model in which consumers choose a brand first, then a product type in the chosen brand, and a typeprimary model in which consumers choose a product type first, and then a brand within that product type.…”

Dynamic Assortment Customization with Limited Inventories

“…Cachon et al (2005) incorporate consumer search costs in a similar context. Kök and Xu (2010) study assortment and pricing decisions in retail categories with multiple subgroups of products. Smith and Agrawal (2000) discuss an optimization approach for assortment selection and inventory management in a multi-item setting with demand substitution.…”