Motivated by the dynamic assortment offerings and item pricings occurring in e-commerce, we study a general problem of allocating finite inventories to heterogeneous customers arriving sequentially. We analyze this problem under the framework of competitive analysis, where the sequence of customers is unknown and does not necessarily follow any pattern. Previous work in this area, studying online matching, advertising, and assortment problems, has focused on the case where each item can only be sold at a single price, resulting in algorithms which achieve the best-possible competitive ratio of 1-1/e. In this paper, we extend all of these results to allow for items having multiple feasible prices. Our algorithms achieve the best-possible weight-dependent competitive ratios, which depend on the sets of feasible prices given in advance. Our algorithms are also simple and intuitive; they are based on constructing a class of universal ``value functions'' which integrate the selection of items and prices offered. Finally, we test our algorithms on the publicly-available hotel data set of Bodea et al. (2009), where there are multiple items (hotel rooms) each with multiple prices (fares at which the room could be sold). We find that applying our algorithms, as a ``hybrid'' with algorithms which attempt to forecast and learn the future transactions, results in the best performance.

中文翻译：

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具有严格的权重相关竞争比的在线匹配，分类和定价算法

受电子商务中出现的动态分类商品和项目定价的激励，我们研究了将有限库存分配给顺序到达的异构客户的一般问题。我们在竞争分析的框架下分析此问题，其中客户的顺序是未知的，不一定遵循任何模式。该领域以前的工作是研究在线匹配，广告和分类问题，该研究的重点是每个商品只能以单一价格出售的情况，从而使算法可以达到1-1 / e的最佳可能竞争比。 。在本文中，我们将所有这些结果扩展为允许具有多个可行价格的商品。我们的算法实现了最佳的，与重量有关的竞争比率，该比率取决于事先给出的可行价格集。我们的算法也简单直观。它们基于构造一类通用的``价值函数''，该函数整合了商品选择和所提供的价格。最后，我们在Bodea等人的公开可用酒店数据集上测试了我们的算法。（2009），其中有多个项目（酒店房间），每个项目都有多个价格（可出售房间的票价）。我们发现，将我们的算法作为尝试与预测和了解未来交易的算法的``混合''应用可以带来最佳性能。那里有多个项目（酒店房间），每个项目都有多个价格（可以出售房间的价格）。我们发现，将我们的算法作为尝试与预测和了解未来交易的算法的``混合''应用可以带来最佳性能。其中有多个项目（酒店房间），每个项目都有多个价格（可以出售该房间的票价）。我们发现，将我们的算法作为尝试与预测和了解未来交易的算法的``混合''应用可以产生最佳性能。