Joint Assortment and Inventory Planning for Heavy Tailed Demand

48 Pages Posted: 26 Apr 2021 Last revised: 26 May 2021

See all articles by Omar El Housni

Omar El Housni

Cornell University - School of Operations Research and Information Engineering

Omar Mouchtaki

Columbia Business School - Decision Risk and Operations

Guillermo Gallego

HKUST

Vineet Goyal

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

Salal Humair

Amazon.com

Sangjo Kim

Shanghai University of Finance and Economics - College of Business

Ali Sadighian

Amazon.com

Jingchen Wu

Amazon.com

Date Written: April 23, 2021

Abstract

We study a joint assortment and inventory optimization problem faced by an online retailer who needs to decide on both the assortment along with the inventories of a set of N substitutable products before the start of the selling season to maximize the expected profit. The problem raises both algorithmic and modeling challenges. One of the main challenges is to tractably model dynamic stock-out based substitution where a customer may substitute to the most preferred product that is available if their first choice is not offered or stocked-out. We first consider the joint assortment and inventory optimization problem for a Markov Chain choice model and present a near-optimal algorithm for the problem. Our results significantly improve over the results in Gallego and Kim (2020) where the regret can be linear in T (where T is the number of customers) in the worst case.

We build upon their approach and give an algorithm with regret Õ(\sqrt{NT}) with respect to an LP upper bound. Our algorithm achieves a good balance between expected revenue and inventory costs 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 customers. We also present a multi-step choice model that captures the complex choice process in an online retail setting characterized by a large universe of products and a heavy-tailed distribution of mean demands. Our model captures different steps of the choice process including search, formation of a consideration set and eventual purchase. We conduct computational experiments that show that our algorithm empirically outperforms previous approaches both on synthetic and realistic instances.

Keywords: Inventory planning, stock-out based substitution, assortment optimization, heavy-tailed demand, sample average approximation, Markov Chain choice model

Suggested Citation

El Housni, Omar and Mouchtaki, Omar and Gallego, Guillermo and Goyal, Vineet and Humair, Salal and Kim, Sangjo and Sadighian, Ali and Wu, Jingchen, Joint Assortment and Inventory Planning for Heavy Tailed Demand (April 23, 2021). Available at SSRN: https://ssrn.com/abstract=3832909 or http://dx.doi.org/10.2139/ssrn.3832909

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/

Omar Mouchtaki (Contact Author)

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Guillermo Gallego

HKUST ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

HOME PAGE: http://https://seng.ust.hk/about/people/faculty/guillermo-gallego

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 ( 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

Amazon.com ( email )

Seattle, WA 98109
United States

Jingchen Wu

Amazon.com ( email )

Seattle, WA 98144
United States

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