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 the modern tool of 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 with probability 1, while (approximately) preserving all of the sales that were prescribed by the fractional solution. In NRM problems, customer substitution induces a negative correlation between products being demanded, making it difficult to apply the standard definition of OCRS. We start by deriving a more powerful notion of "random-element" OCRS that achieves a guarantee of 1/(1+L) for NRM with customer substitution, matching a common benchmark in the literature. We show this benchmark is unbeatable for all integers L that are the power of a prime number. We then show how to beat this benchmark under three widely applied assumptions. Finally, we show that under several assumptions, it is possible to do better than offline CRS when L>= 5. 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 having no substitution. Our result under the assumption that products comprise one item from each of up to L groups implies that 1/(1+L) can be beaten for Prophet Inequality on the intersection of L partition matroids, a problem of interest. In sum, our paper shows how to apply OCRS to all of these problems and establishes a surprising separation in the achievable guarantees when substitution is involved, under general resource constraints parametrized by L.

翻译：在网络收益管理（NRM）问题中，由最多L种资源构成的产品被出售给随机到达的客户。受现代工具——在线竞争解决方案（OCRS）的启发，我们采用随机舍入方法处理NRM问题。其目标是获取一个满足资源约束期望值的NRM分数解，并通过在线策略以概率1实现资源约束，同时（近似地）保留分数解所规定的所有销售。在NRM问题中，客户替代会导致产品需求间产生负相关性，这使得应用OCRS的标准定义变得困难。我们首先推导出一种更强大的“随机元素”OCRS概念，该方案能在存在客户替代的情况下为NRM实现1/(1+L)的保证，达到了文献中常见的基准。我们证明对于所有为质数幂的整数L，该基准是不可超越的。随后，我们展示了在三种广泛应用假设下如何突破这一基准。最后，我们证明在若干假设下，当L≥5时，有可能获得优于离线CRS的结果。我们的研究结果对在线组合拍卖具有相应启示，其中买家对最多包含L件商品的组合进行竞价，而买家的单一需求特性类似于不存在替代的情况。在假设产品由最多L个组中各取一件商品构成的前提下，我们的结果表明可以在L个划分拟阵交集的先知不等式问题上突破1/(1+L)的界限，这是一个值得关注的问题。总之，本文展示了如何将OCRS应用于所有这些问题，并在涉及替代的情况下，建立了以L为参数的一般资源约束条件下可达成保证的惊人分离。