Algorithms for Online Matching, Assortment, and Pricing with Tight Weight-dependent Competitive Ratios

TL;DR

This paper develops algorithms for online inventory allocation that handle multiple prices per item, achieving optimal weight-dependent competitive ratios and demonstrating superior performance on hotel booking data.

Contribution

It extends existing online matching algorithms to multiple pricing options, achieving optimal weight-dependent competitive ratios with simple, universal value functions.

Findings

Algorithms achieve the best-possible weight-dependent competitive ratios.

Hybrid approach with forecasting algorithms improves performance.

Validated on hotel data set with multiple items and prices.

Abstract

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.