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Prof. Fernando G. Bernstein
Bob J. White Professor
The Fuqua School of Business
Duke University

This paper focuses on subscription box services in which a provider selects the assortment of products to include in the box by taking into account the customer’s preferences. Customers interested in purchasing a product choose between engaging in active search (i.e., visit physical stores) or subscribing to a box delivery service. We study the subscription box company’s problem of selecting the optimal contents of the box to maximize expected revenue (by driving demand from customers). Since a product may be both available at a store and included in the box, the assortment in a box affects the set of stores that a customer would visit under active search and therefore the customer’s subscription decision. We model such interaction by applying a cross-nested logit framework that correlates the contents in the box with the products available at the stores. We find that the box should include a collection of popular subsets of the store products for customers that experience a relatively low or relatively high search cost. If a preview of the box is available, we find that, for customers with intermediate values of the search cost, it may be optimal to include a so-called utility loss leader, i.e., a product with relatively low valuation, to entice customers to subscribe to the box delivery service and therefore increase the likelihood of a sale. We use rational expectations to model a setting in which a preview of the box is not available. We also examine the decision of offering exclusive products in addition to branded items.