Assortment Optimization for a Multi-Stage Choice Model
Manufacturing & Service Operations Management
55 Pages Posted: 23 Sep 2018 Last revised: 12 Apr 2023
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
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