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.

翻译：在网络收入管理（NRM）问题中，由最多L种资源组成的产品被销售给随机抵达的客户。受在线竞争解决机制（OCRS）发展的启发，我们采用随机取整方法处理NRM。目标是获取满足期望资源约束的分数解，并通过在线策略在任意状态下实现资源约束，同时（近似）保留分数解所规定的所有销售。OCRS无法被直接应用于NRM或一般的收入管理问题，因为客户替代会在产品需求中引入负相关性。我们首先推导出一个OCRS，在存在客户替代的情况下实现1/(1+L)的保证，这与文献中的常见基准一致。随后，我们展示如何在无替代假设下（即标准OCRS设置）对所有整数L>1超越这一基准。相比之下，我们证明当存在客户替代时，对于所有为素数幂的整数L，使用OCRS或任何分数松弛都无法击败该基准。最后，我们展示即使存在客户替代，如果产品由最多L个组中各选一个物品组成，仍可超越1/(1+L)。我们的结果对在线组合拍卖具有相应启示，其中买家竞拍最多L个物品的组合，而单目标买家类似于无替代情况。最终结果还在L个划分拟阵的交集上超越了预言不等式中的1/(1+L)。总体而言，本文为将OCRS应用于这些问题提供了统一框架，阐明了替代的影响，并建立了以L为参数的一般资源约束下有无替代所能实现保证的分离。