Omar El Housni – Mathematics and Decision

$\begin{quote} \begin{center} \textbf{Joint Inventory Optimization and Assortment Personalization} \end{center} \medskip In this talk, we give approximation algorithms for a joint inventory allocation and assortment personalization problem motivated by an online retail setting. In our problem, we have a limited amount of storage capacity that needs to be allocated among multiple products to serve customers that arrive over a selling horizon. At the beginning of the selling horizon, we decide how many units of each product to stock. Over the selling horizon, customers arrive at the platform one by one to make a purchase. Based on the remaining inventories of the products and the information available on the arriving customer, we offer a personalized assortment of products to each customer. The customer either makes a choice within the offered assortment or leaves without a purchase. Our goal is to decide how many units of each product to stock at the beginning of the selling horizon and to find a policy to figure out which personalized assortment to offer to each arriving customer to maximize the total expected revenue over the selling horizon. Allocating the storage capacity among the products requires tackling a combinatorial optimization problem, whereas finding an assortment personalization policy requires approximating a dynamic program with a high-dimensional state variable. We develop an algorithmic approximation framework that gives the first theoretical guarantees for this class of problems. Our framework builds on techniques from submodular optimization and dynamic programming. \end{quote}$