Joint Assortment and Inventory Planning under the Markov chain Choice Model

Abstract

We address the joint assortment and inventory optimization problem for an online retailer facing a set of N substitutable products. The retailer must determine both the assortment and inventories of these products before the start of the selling season to maximize the expected profit. We consider a setting with dynamic stock-out-based substitution, where consumers' choices follow the Markov chain choice model. This is a challenging problem, and even computing the expected profit for a given assortment and inventory solution requires solving an intractable dynamic program. We present a sample average approximation-based algorithm for the problem that achieves a regret of Õ(√ N T) with respect to an LP upper bound. Our algorithm first selects an assortment by balancing the expected revenue (from a single consumer) and the inventory cost. We do this by identifying a subset of products that can pool demand from the universe of substitutable products without significantly cannibalizing the revenue in the presence of dynamic substitution behavior of consumers. We then use a sample average approximation-based LP to decide the inventory level for each item in the selected assortment. We numerically show that our algorithm considerably improves the performance over standard approaches from the literature on a wide range of instances of the Markov chain choice model and demonstrate that it handles carefully the inventory of products in the long tail (i.e., products with small mean total demand).

Keywords: Inventory planning, stock-out-based substitution, Markov chain choice model, assortment optimization, sample average approximation