ecommerce platform operators

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.

Abstract: We study an intermediary that buys nonperishing items from arriving sellers and sells them to arriving buyers, subject to limited storage. Sellers and buyers arrive according to independent Poisson processes. The intermediary pays and charges the same fixed item prices, aiming to maximize long-run gains from trade: buyer value minus seller cost. Our benchmark may choose allocations directly, has unlimited storage, and must purchase each unit before allocating it. Its optimal long-run gain rate equals the value of a linear program of average purchase and allocation rates, with or without knowledge of future arrivals. For buyers whose bundle values are maxima of nonnegative additive valuations (XOS), we compute static common prices that guarantee half of this benchmark for arbitrary finite item capacities, even one storage slot per item, regardless of how ties are resolved without using future arrivals. The prices are computable in polynomial time using demand and supporting-value queries. The construction equalizes itemwise lower bounds on buyer and seller contributions to gains from trade, accounting for procurement costs. We call this contribution balance. As a single-item foundation, we also equalize the rates of purchases and sales selected by the price, before checking inventory availability. We call this rate balance. For capacity $C$, it yields the tight guarantee $C/(C+1)$. The two principles parallel proofs of the classical prophet inequality based on half the expected benchmark and on a median threshold, adapting these balancing ideas to recurring two-sided markets with limited inventory.

Abstract: We study online assortment optimization under Markov chain choice and independent Bernoulli arrivals, with each period's request type known in advance. Each product may have multiple interchangeable physical copies, and each booking reserves consecutive service slots on a single copy. Customers choose among products, while the platform assigns purchases to feasible copies. We develop a sales-based relaxation that upper-bounds the optimal online revenue and use it to design a policy with two components: independent sampling and purchase--update coupling. We generate independent copy proposals and make a product eligible whenever at least one of its copies proposes. A general revenue-extraction bound for random candidate sets with independent product inclusions shows that optimizing over eligible products recovers at least half of each period's relaxation revenue benchmark in expectation. A purchase--update coupling reproduces the interval flows through independent virtual copy updates while preserving physical feasibility. Under general Markov chain choice, the policy uses a random gate to make the coupling feasible: it offers the selected assortment with probability \(1-1/e\) and the empty assortment otherwise. No gate is needed under multinomial logit (MNL) choice. The resulting policies achieve approximation ratios of \((1-1/e)/2\) and \(1/2\), respectively, relative to the optimal nonanticipative online policy, independently of product capacities. In the single-copy MNL setting, our policy improves the guarantee of \citet{huwu2026} from \(0.271\) to \(1/2\) under the same arrival convention. The \(1/2\) static extraction factor and the \(1-1/e\) uniform scalar-gate factor are separately sharp, and the \(1/2\) MNL guarantee is tight for the proposed policy.

Abstract: Product families in large product catalogs suffer from inconsistencies such as duplicates and unit mismatches that degrade customer experience. Detecting these requires reasoning over multiple error types across lengthy product listings, where LLM classification quality degrades due to long-context limitations. We address this by decomposing detection into focused sub-tasks that reduce context and isolate error types, improving F1 from 52\% to 87\%. For scalable deployment, we introduce Positional Task Conditioning (PTC), which distills this capability into a single smaller model by reinforcing task identity at structural prompt boundaries. PTC outperforms rationale-based distillation across five models and two architecture families, achieving within 1.79\% F1 of the frontier at upto 98\% lower cost. Our system is deployed across multiple countries processing 10+ million product families.