Personalized Assortment Optimization for a Subscription Business Model of Experience Goods

Abstract

Motivated by rental fashion businesses, we investigate personalized assortment optimization for a multi-item subscription business model of experience goods. In this context, the firm faces (i) initial selection uncertainty about customers' subscription decision and subsequent basket selection, and (ii) renewal uncertainty regarding customers' decision to renew their subscription based on their realized product fit experience.  We develop a two-period decision model that captures these salient characteristics and considers customers' multi-item basket choices. This results in a nested combinatorial assortment optimization problem for the profit-maximizing firm, which reduces to a signal-to-noise maximization problem in the simple case where there is no initial selection uncertainty about a customer's subscription decision. To facilitate solving the general problem, we derive lower and upper bounds on the expected profit. The lower bound is tight when the basket size is equal to the recommendation set size, and the upper bound provides a good approximation when the basket size is one. Building on these results, we propose efficient algorithms to solve the problem and provide some analytical insights into how they operate. Extensive numerical experiments demonstrate that our algorithms run four orders of magnitude faster than the brute-force method while achieving results within 6.5% of the optimal expected profit for a range of randomly generated problem instances.

Keywords: assortment optimization, subscription business model, experience goods, survival analysis