Dynamic Assortment with Online Learning Under Threshold Multinomial Logit Model

53 Pages Posted: 30 May 2024 Last revised: 22 Oct 2024

See all articles by Wenxiang Chen

Wenxiang Chen

School of Management and Engineering, Nanjing University

Caihua Chen

School of Management and Engineering, Nanjing University

Houcai Shen

Nanjing University - School of Management and Engineering

Ruxian Wang

Johns Hopkins University - Carey Business School

Weili Xue

Southeast University

Date Written: May 28, 2024

Abstract

Consumers often find themselves overwhelmed by extensive assortments offered by  retailers and therefore may exhibit bounded rationality in their purchase decisions. However, existing literature on dynamic assortment optimization barely consider consumers' such bounded rational behavior. This motivates us to employ a simple but effective two-stage consider-then-choose model, namely the Threshold Multinomial Logit (TMNL) model to investigate the assortment optimization problem. The TMNL model characterizes consumers' endogenous consideration sets formation by the threshold effect. This endogenous dependency can capture more flexible substitution patterns than the classical MNL choice model, but it also creates great difficulties for online learning. In the offline assortment setting, we analyze the properties of optimal assortment and propose an efficient assortment optimization algorithm that outperforms the benchmark. In the online setting with unknown customer preferences and consideration set formation, we propose online learning algorithms that achieve nearly optimal regret bounds in both instance-independent and instance-dependent conditions. To the best of our knowledge, this is the first work to consider online assortment problems with consumers' endogenous consider-then-choose behavior. Moreover, our algorithm is extended to the contextual learning setting that effectively mitigates the impact of the number of products on performance. Extensive numerical experiments further validate the efficacy of our proposed algorithms.

Keywords: Online Learning, Threshold Effect, Consideration Set, Assortment Optimization, Bandit Algorithms

Suggested Citation

Chen, Wenxiang and Chen, Caihua and Shen, Houcai and Wang, Ruxian and Xue, Weili, Dynamic Assortment with Online Learning Under Threshold Multinomial Logit Model (May 28, 2024). Available at SSRN: https://ssrn.com/abstract=4844426 or http://dx.doi.org/10.2139/ssrn.4844426

Wenxiang Chen

School of Management and Engineering, Nanjing University ( email )

Nanjing
China

Caihua Chen

School of Management and Engineering, Nanjing University ( email )

Nanjing
China

Houcai Shen

Nanjing University - School of Management and Engineering ( email )

Nanjing, 210093
China

Ruxian Wang (Contact Author)

Johns Hopkins University - Carey Business School ( email )

1625 Massachusetts Ave NW
Washington, DC 20036
United States

Weili Xue

Southeast University ( email )

Banani, Dhaka, Bangladesh
Dhaka
Bangladesh

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