Assortment Optimization for the Multinomial Logit Model with Repeated Customer Interactions

45 Pages Posted: 2 Aug 2023 Last revised: 4 Aug 2023

See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto - Rotman School of Management

Pin Gao

School of Data Science, The Chinese University of Hong Kong, Shenzhen

Chenhao Wang

Chinese University of Hong Kong, Shenzhen

Yao Wang

Xi'an Jiaotong University (XJTU)

Date Written: July 31, 2023

Abstract

This paper presents the multinomial logit model with repeated customer interactions. In each period, the same customer selects a product from the assortment recommended in that period or opts out. It captures the essence of an increasingly popular business model called the subscription box, exemplified by Stitch Fix and Wantable. From the seller's perspective, the choice probability is updated based on the purchase history. We study the adaptive assortment recommendation strategy for all the periods. Although the problem is generally NP-hard as we show, when the customer interacts with the seller for two periods, we discover the structures of the optimal assortment when the available products in the two periods are identical and develop approximation algorithms in other cases. For more than two periods, although the optimal assortments are intractable, we find that the optimal fixed assortments that are not adapted to the purchase history can achieve 68.47% or 50% of the optimal expected revenue, respectively, when the available products across periods are disjoint or not. Using two public datasets, we demonstrate that the model with repeated customer interactions can better predict the purchase behavior and generates higher revenues.

Keywords: repeated customer interactions, multinomial logit, sequential recommendation, assortment optimization, discrete choice models

Suggested Citation

Chen, Ningyuan and Gao, Pin and Wang, Chenhao and Wang, Yao, Assortment Optimization for the Multinomial Logit Model with Repeated Customer Interactions (July 31, 2023). Available at SSRN: https://ssrn.com/abstract=4526247 or http://dx.doi.org/10.2139/ssrn.4526247

Ningyuan Chen (Contact Author)

University of Toronto - Rotman School of Management ( email )

Pin Gao

School of Data Science, The Chinese University of Hong Kong, Shenzhen ( email )

Chenhao Wang

Chinese University of Hong Kong, Shenzhen ( email )

2001 Longxiang Boulevard, Longgang District
Shenzhen, 518172

Yao Wang

Xi'an Jiaotong University (XJTU)

26 Xianning W Rd.
Xi'an Jiao Tong University
Xi'an, Shaanxi 710049
China

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