Assortment Optimization for a Multi-Stage Choice Model

Manufacturing & Service Operations Management

55 Pages Posted: 23 Sep 2018 Last revised: 12 Apr 2023

See all articles by Yunzong Xu

Yunzong Xu

Massachusetts Institute of Technology (MIT)

Zizhuo Wang

The Chinese University of Hong Kong, Shenzhen

Date Written: September 4, 2018

Abstract

Problem definition: Motivated by several practical selling scenarios that require previous purchases to unlock future options, we consider a multi-stage assortment optimization problem, where the seller makes sequential assortment decisions with commitment, and the customer makes sequential choices to maximize her expected utility.

Methodology/results: We start with the two-stage problem and formulate it as a dynamic combinatorial optimization problem. We show that this problem is polynomial-time solvable when
the customer is fully myopic or fully forward-looking. In particular, when the customer is fully forward-looking, the optimal policy entails that the assortment in each stage is revenue-ordered
and a product with higher revenue always leads to a wider range of future options. Moreover, we find that the optimal assortment in the first stage must be smaller than the optimal assortment when there were no second stage and the optimal assortment in the second stage must be larger than the optimal assortment when there were no first stage. When the customer is partially forward-looking, we show that the problem is NP-hard in general. In this case, we establish the polynomial-time solvability under certain conditions. In addition, we propose a 2-approximation algorithm in the general setting. We further extend the above results to the multi-stage problem with an arbitrary number of stages, for which we derive generalized structural properties and efficient algorithms.

Managerial implications: Firms can benefit from our study and improve their sequential assortment strategies when their interaction with each customer consists of multiple stages.

Keywords: Multi-Stage Choice Model, Assortment Optimization, Revenue Management

Suggested Citation

Xu, Yunzong and Wang, Zizhuo, Assortment Optimization for a Multi-Stage Choice Model (September 4, 2018). Manufacturing & Service Operations Management, Available at SSRN: https://ssrn.com/abstract=3243742 or http://dx.doi.org/10.2139/ssrn.3243742

Yunzong Xu

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Zizhuo Wang (Contact Author)

The Chinese University of Hong Kong, Shenzhen ( email )

2001 Longxiang Road
Longgang District
Shenzhen, Guangdong 517182
China

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