Exploration versus exploitation in assortment optimization with limited inventory and substitutable demand

This study considers an online multi-period assortment optimization problem over multiple replenishment cycles where the seller chooses a subset from N substitutable products and decides the limited amount of each to order and sell at every period. The seller is constrained by a total inventory capacity, a cardinality constraint on the product variety (shelf space), and predetermined replenishment time intervals. The assortment selection is modeled as a Multi-armed bandit problem and the customers' choice is modeled by the MNL choice model. The objective is to optimize the revenue by learning the demand parameters and improve the offering composition at every period. In this novel approach, the offering and consequently the exploration-exploitation decision has two dimensions: the assortment and the inventory allocation. The present research develops a model and policy for learning and optimization that demonstrates good performance in numerical simulations. The results suggest that capacity constraint has a significant impact on the total profit of a seller who tries to learn the demand and the best inventory composition on the fly.