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

54 Pages Posted: 20 Jun 2017 Last revised: 17 Feb 2019

See all articles by Will Ma

Will Ma

Massachusetts Institute of Technology (MIT)

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Date Written: June 19, 2017

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.

Keywords: Online Algorithms, Competitive Ratio, Revenue Management, Online Matching, Adwords, Booking Limits

Suggested Citation

Ma, Will and Simchi-Levi, David, Algorithms for Online Matching, Assortment, and Pricing with Tight Weight-dependent Competitive Ratios (June 19, 2017). Available at SSRN: https://ssrn.com/abstract=2989332 or http://dx.doi.org/10.2139/ssrn.2989332

Will Ma (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

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