Online Resource Allocation under Arbitrary Arrivals: Optimal Algorithms and Tight Competitive Ratios

52 Pages Posted: 20 Jun 2017 Last revised: 1 Jun 2018

Will Ma

Massachusetts Institute of Technology (MIT)

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Date Written: June 19, 2017

Abstract

We consider the problem of allocating fixed resources to heterogeneous customers arriving sequentially. We study this problem under the framework of competitive analysis, which does not assume any predictability in the sequence of customer arrivals. Previous work has culminated in optimal algorithms under two scenarios: (i) there are multiple resources, each of which yields reward at a constant rate when allocated; or (ii) there is a single resource, which yields reward at different rates when allocated to different customers.

In this paper, we derive optimal allocation algorithms when there are multiple resources, each with multiple reward rates. Our algorithms are simple, intuitive, and robust against forecast error. Their tight competitive ratio cannot be achieved by combining existing algorithms, which consider the tradeoffs between multiple resources and multiple reward rates separately.

By showing how to integrate these tradeoffs while making allocation decisions, we expand the applicability of competitive analysis in many areas, such as online advertising, matching markets, and personalized e-commerce. We test our methodological contribution on the hotel data set of Bodea et al. (2009), where there are multiple resources (hotel rooms), each with multiple reward rates (fares at which the room could be sold). We find that applying our algorithms, in conjunction 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, Online Resource Allocation under Arbitrary Arrivals: Optimal Algorithms and Tight 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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