A Unified Framework for Assortment Optimization and Matching under MNL Choice
Omar El Housni, Ulysse Hennebelle
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.
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