Robust Assortment Optimization Under the Markov Chain Choice Model

Désir, Antoine; Goyal, Vineet; Jiang, Bo; Xie, Tian; Zhang, Jiawei

doi:10.1287/opre.2022.2420

Cited by 5 publications

(1 citation statement)

References 41 publications

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“…Désir et al. (2015) study the robust assortment optimization under this model. As described in the introduction, the STCM we propose differs from the Markov chain choice model in two dimensions: (i) we add a control for the seller to decide which set of products to recommend when customers arrive at an unavailable product, and (ii) we only allow a single transition of the customers.…”

Section: Related Workmentioning

confidence: 99%

Assortment Optimization under a Single Transition Choice Model

Nip

Wang

2021

Production and Operations Management

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In this study, we consider a new customer choice model which we call the single transition choice model. In this model, there is a universe of products and customers arrive at each product with a certain probability. If the arrived product is unavailable, then the seller can recommend a subset of available products and the customer will purchase one of the recommended products or choose not to purchase with certain transition probabilities. The distinguishing features of the model are that the seller can control which products to recommend depending on the arrived product, and each customer either purchases a product or leaves the market after one transition. We study the assortment optimization problem under this model. Particularly, we show that it is NP‐Hard even if the customer can transition from each product to at most two products. Despite the computational complexity, we provide polynomial time algorithms or approximation algorithms for several special cases, such as when the customer can only transition from each product to at most a given number of products and the size of each recommended set is bounded. Our approximation algorithms are developed by invoking the submodularity arguments, or connecting the problem with maximum constraint satisfaction problem and applying randomized rounding techniques to its semidefinite programming relaxation. We also provide a tight worst‐case performance bound for revenue‐ordered assortments. In addition, we propose a compact mixed‐integer program formulation, which is efficient for moderate size problems. Finally, we conduct numerical experiments to demonstrate the effectiveness of the proposed algorithms.

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Section: Related Workmentioning

confidence: 99%

Assortment Optimization under a Single Transition Choice Model

Nip

Wang

2021

Production and Operations Management

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Assortment optimization: a systematic literature review

Heger,

Klein

2024

OR Spectrum

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Assortment optimization is a core topic of demand management that finds application in a broad set of different areas including retail, airline, hotel, and transportation industries as well as in the healthcare sector. Hence, the interest in research on assortment optimization has grown rapidly in recent years. However, the sheer number of publications on the topic of assortment optimization makes it difficult to keep track of all available approaches proposed in the literature. In this paper, we systematically review state-of-the-art studies on assortment optimization. We assemble an extensive literature overview by strategically searching for pre-defined keywords within leading scientific databases. The resulting literature is grouped by a proposed taxonomy that captures properties related to the optimization problem itself, the modelled customer behaviour, and the solution concept applied for solving the problem at hand. For each group, we provide an overview of the corresponding literature and analyse it based on a proposed selection of key factors.

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Randomized Assortment Optimization

Wang,

Peura,

Wiesemann

2024

Operations Research

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When a firm selects an assortment of products to offer to customers, it uses a choice model to anticipate their probability of purchasing each product. In practice, the estimation of these models is subject to statistical errors, which may lead to significantly suboptimal assortment decisions. In “Randomized Assortment Optimization,” Wang, Peura, and Wiesemann show that the standard approach of deterministically selecting a single assortment to offer is not always optimal in this setting: Instead, the firm can do better by selecting an assortment randomly according to a prudently designed probability distribution. The authors show how an optimal randomization strategy can be determined for common choice models, improving performance in realistic data-driven settings. The results suggest that more general versions of the assortment optimization problem—incorporating business constraints, more flexible choice models and/or more general forms of uncertainty—tend to be more receptive to the benefits of randomization.

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Robust Assortment Optimization Under the Markov Chain Choice Model

Cited by 5 publications

References 41 publications

Assortment Optimization under a Single Transition Choice Model

Assortment Optimization under a Single Transition Choice Model

Assortment optimization: a systematic literature review

Randomized Assortment Optimization

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