A Unified Framework for Assortment Optimization and Matching under MNL Choice
Abstract
We develop a unified framework for assortment optimization and matching under multinomial logit (MNL) choice, yielding simple algorithms and analyses across a broad class of problems. The framework centers on a single-customer assortment problem in which the firm commits to eligible products before their independent availabilities are revealed. A simple threshold policy achieves a tight 1/2 guarantee against a benchmark that selects its assortment after observing availability and may control dependence subject to the same marginal probability bounds. This guarantee accommodates cardinality constraints and adversarial removal of excess available products. Combined with problem-specific linear programming relaxations, the framework yields 1/2 guarantees for standard two-sided assortment optimization, customization under mixtures of MNL models, ride-hailing notifications, multi-round broadcast matching, and MNL prophet inequalities, and a 1/4 guarantee for fully static two-sided assortment optimization. Across these applications, we improve approximation factors, extend guarantees to more general revenues and cardinality constraints, and retain existing factors against stronger benchmarks.
Related
- Inventory and Assortment Optimization under General Choice: A Unified Approximation Framework
- Canonical Exponential-Family Mixtures for Latent Class Choice Models: A Unified Closed-Form EM Framework, with the Gaussian–Geometric Case
- Centered Weak Discrete Riemannian Gradients: A Unified Framework for Riemannian Optimization
- AI-Mediation in Retail Markets: Revenue Effects and Assortment Optimization
- Assortment optimization under the perception-adjusted Luce model
BibTeX
@misc{housni2026unified,
title = {{A Unified Framework for Assortment Optimization and Matching under MNL Choice}},
author = {Omar El Housni and Ulysse Hennebelle},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35389},
eprint = {2610.35389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35389},
}
RIS
TY - UNPB
TI - A Unified Framework for Assortment Optimization and Matching under MNL Choice
AU - Omar El Housni
AU - Ulysse Hennebelle
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35389
UR - https://arxiv.org/abs/2610.35389
AB - We develop a unified framework for assortment optimization and matching under multinomial logit (MNL) choice, yielding simple algorithms and analyses across a broad class of problems. The framework centers on a single-customer assortment problem in which the firm commits to eligible products before their independent availabilities are revealed. A simple threshold policy achieves a tight 1/2 guarantee against a benchmark that selects its assortment after observing availability and may control dependence subject to the same marginal probability bounds. This guarantee accommodates cardinality constraints and adversarial removal of excess available products. Combined with problem-specific linear programming relaxations, the framework yields 1/2 guarantees for standard two-sided assortment optimization, customization under mixtures of MNL models, ride-hailing notifications, multi-round broadcast matching, and MNL prophet inequalities, and a 1/4 guarantee for fully static two-sided assortment optimization. Across these applications, we improve approximation factors, extend guarantees to more general revenues and cardinality constraints, and retain existing factors against stronger benchmarks.
ER -