Joint Assortment and Inventory Planning under the Markov chain Choice Model

45 Pages Posted: 26 Apr 2021 Last revised: 5 Jun 2023

See all articles by Omar Mouchtaki

Omar Mouchtaki

New York University (NYU) - Leonard N. Stern School of Business

Omar El Housni

Cornell University - School of Operations Research and Information Engineering

Guillermo Gallego

CUHK-SZ

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Salal Humair

Amazon.com, Inc.

Sangjo Kim

Shanghai University of Finance and Economics - College of Business

Ali Sadighian

Uber Inc

Jingchen Wu

Flexport

Date Written: April 23, 2021

Abstract

We address the joint assortment and inventory optimization 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(\sqrt{NT}) 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 (note that we incur inventory cost with probability one while we get revenue only when an item is sold). 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

Suggested Citation

Mouchtaki, Omar and El Housni, Omar and Gallego, Guillermo and Goyal, Vineet and Humair, Salal and Kim, Sangjo and Sadighian, Ali and Wu, Jingchen, Joint Assortment and Inventory Planning under the Markov chain Choice Model (April 23, 2021). Columbia Business School Research Paper Forthcoming, Available at SSRN: https://ssrn.com/abstract=3832909 or http://dx.doi.org/10.2139/ssrn.3832909

Omar Mouchtaki (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
New York, NY NY 10012
United States

Omar El Housni

Cornell University - School of Operations Research and Information Engineering ( email )

2 E Loop Rd
New York, NY 10044
United States

HOME PAGE: http://https://people.orie.cornell.edu/oe46/

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Salal Humair

Amazon.com, Inc. ( email )

Seattle, WA 98144
United States

Sangjo Kim

Shanghai University of Finance and Economics - College of Business ( email )

777 Guoding Road
Shanghai, 200433
China

Ali Sadighian

Uber Inc ( email )

NY
United States

Jingchen Wu

Flexport ( email )

San Francisco, CA 94102
United States

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