On the relationship between inventory costs and variety benefits in retail assortments

Consider a category of product variants distinguished by some attribute such as color or flavor. A retailer must construct an assortment for the category, i.e., select a subset of variants to stock and determine purchase quantities for each offered variant. We analyze this problem using a multinomial logit model to describe the consumer choice process and a newsboy model to represent the retailer's inventory cost. We show that the optimal assortment has a simple structure and provide insights on how various factors affect the optimal level of assortment variety. We also develop a formal definition of the level of fashion in a category using the theory of majorization and examine its implications for category profits.