2019/05/12 by Will Ma, David Simchi‐Levi, Ma, Will +1 · 1 citation
Business, Management and Accounting · Computer Science · Decision Sciences · #Auction Theory and Applications #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Optimization and Search Problems #Supply Chain and Inventory Management
paper · pdf · doi:10.48550/arxiv.1905.04770
openalex publication_date 2019/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.