The Exponomial Choice Model for Assortment Optimization: An Alternative to the MNL Model?

Ali Aouad, Jacob Feldman*, Danny Segev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the yet-uncharted assortment optimization problem under the exponomial choice model, in which the objective is to determine the revenue-maximizing set of products that should be offered to customers. Our main algorithmic contribution comes in the form of a fully polynomial-time approximation scheme, showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. We synthesize several ideas related to approximate dynamic programming, intended to construct a compact discretization of the continuous state space by keeping track of “key statistics” in rounded form and by operating with a suitable bit precision complexity. We complement this result by a number of NP-hardness reductions to natural extensions of this problem. Moreover, we conduct empirical and computational evaluations of the exponomial choice model and our solution method. Focusing on choice models with a simple parametric structure, we provide new empirical evidence that the exponomial choice model can achieve higher predictive accuracy than the multinomial logit (MNL) choice model on several real-world data sets. We uncover that this predictive performance correlates with certain characteristics of the choice instance—namely, the entropy and magnitude of choice probabilities. Finally, we leverage fully ranked preference data to simulate the expected revenue of optimal assortments prescribed using the fitted exponomial and MNL models. On semisynthetic data, the exponomial-based approach can lift revenues by 3%–4% on average against the corresponding MNL benchmark.

Original languageEnglish
Pages (from-to)2814-2832
Number of pages19
JournalManagement Science
Volume69
Issue number5
DOIs
StatePublished - May 2023

Funding

FundersFunder number
Israel Science Foundation1407/20, 148/10

    Keywords

    • FPTAS
    • approximate dynamic programming
    • assortment optimization
    • case study

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