Dynamic Assortment Selection Under Inventory and Limited Switches Constraints

Optimizing the assortment of products to display to customers is key to increasing revenue for both offline and online retailers. To trade-off between exploring customers' preferences and exploiting customers' choices learned from data, in this article, by adopting the Multi-Nomial Logit (MNL) choice model to capture customers' choices over products, we study the problem of optimizing assortments over a planning horizon T for maximizing the profit of the retailer. To make the problem setting more practical, we consider both the inventory constraint and the limited switches constraint, where the retailer is forced to stop the sales when the resources are depleted and is forbidden to switch the assortment shown to customers too many times. Such a setting suits the case when an online retailer wants to optimize the assortment selection for a population of customers dynamically. We develop an efficient UCB-like algorithm to optimize the assortments while learning customers' choices from data. We prove that our algorithm can achieve a sub-linear regret bound (O) over tilde (T-max{2/3-alpha/3,T-1/2}) if O(T-alpha) switches are allowed. Extensive numerical experiments show that our algorithm outperforms baselines, and the gap between our algorithm's performance and the theoretical upper bound is small.