Online Contention Resolution Schemes for Network Revenue Management and Combinatorial Auctions

In the Network Revenue Management (NRM) problem, products composed of up to L resources are sold to stochastically arriving customers. We take a randomized rounding approach to NRM, motivated by developments in Online Contention Resolution Schemes (OCRS). The goal is to take a fractional solution to NRM that satisfies the resource constraints in expectation, and implement it in an online policy that satisfies the resource constraints in any state, while (approximately) preserving all of the sales that were prescribed by the fractional solution. OCRS cannot be naively applied to NRM or revenue management problems in general, because customer substitution induces a negative correlation in products being demanded. We start by deriving an OCRS that achieves a guarantee of 1/(1+L) for NRM with customer substitution, matching a common benchmark in the literature. We then show how to beat this benchmark for all integers L>1 assuming no substitution, i.e., in the standard OCRS setting. By contrast, we show that this benchmark is unbeatable using OCRS or any fractional relaxation if there is customer substitution, for all integers L that are the power of a prime number. Finally, we show how to beat 1/(1+L) even with customer substitution, if the products comprise one item from each of up to L groups. Our results have corresponding implications for Online Combinatorial Auctions, in which buyers bid for bundles of up to L items, and buyers being single-minded is akin to no substitution. Our final result also beats 1/(1+L) for Prophet Inequality on the intersection of L partition matroids. All in all, our paper provides a unifying framework for applying OCRS to these problems, delineating the impact of substitution, and establishing a separation between the guarantees achievable with vs. without substitution under general resource constraints parametrized by L.