Exact Logit-Based Product Design

Akçakuş, İrem; Mišić, Velibor V.

doi:10.48550/arxiv.2106.15084

Cited by 1 publication

(1 citation statement)

References 38 publications

(56 reference statements)

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“…Notably, this is a common and natural assumption in the existing literature when providing FPTAS results for the assortment optimization problem under various choice models (Désir et al 2022, Akçakuş and and sum-of-ratios optimization (Rusmevichientong et al 2009, Mittal andSchulz 2013). In particular, Désir et al (2022) and Akçakuş and Mišić (2021) also consider a discretize-then-approximate approach, where they discretize the utility parameters of the LC-MNL model.…”

Section: Value Function: Jmentioning

confidence: 99%

A Nonparametric Stochastic Set Model: Identification, Optimization, and Prediction

Chen¹,

Митрофанов²

2023

Preprint

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The identification of choice models is crucial for understanding consumer behavior and informing marketing or operational strategies, policy design, and product development. The identification of parametric choicebased demand models is typically straightforward. However, nonparametric models, which are highly effective and flexible in explaining customer choice, may encounter the challenge of the dimensionality curse, hindering their identification. A prominent example of a nonparametric model is the ranking-based model, which mirrors the random utility maximization (RUM) class and is known to be nonidentifiable from the collection of choice probabilities alone. Our objective in this paper is to develop a new class of nonparametric models that is not subject to the problem of nonidentifiability. Our model assumes bounded rationality of consumers, which results in symmetric demand cannibalization and intriguingly enables full identification. Additionally, our choice model demonstrates competitive prediction accuracy compared to the state-of-the-art benchmarks in a real-world case study, despite incorporating the assumption of bounded rationality which could, in theory, limit the representation power of our model.In addition, we tackle the important problem of finding the optimal assortment under the proposed choice model. We demonstrate the NP-hardness of this problem and provide a fully polynomial-time approximation scheme through dynamic programming. Additionally, we propose an efficient estimation framework using a combination of column generation and expectation-maximization algorithms, which proves to be more tractable than the estimation algorithm of the aforementioned ranking-based model.

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Section: Value Function: Jmentioning

confidence: 99%