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Dynamic Relaxations for Online Bipartite Matching

Author

Listed:
  • Alfredo Torrico

    (CERC in Data Science, Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Montréal, Quebec H2V 4G9, Canada)

  • Alejandro Toriello

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

Online bipartite matching (OBM) is a fundamental model underpinning many important applications, including search engine advertisement, website banner and pop-up ads, and ride hailing. We study the independent and identically distributed (i.i.d.) OBM problem, in which one side of the bipartition is fixed and known in advance, whereas nodes from the other side appear sequentially as i.i.d. realizations of an underlying distribution and must immediately be matched or discarded. We introduce dynamic relaxations of the set of achievable matching probabilities; show how they theoretically dominate lower dimensional, static relaxations from previous work; and perform a polyhedral study to theoretically examine the new relaxations’ strength. We also discuss how to derive heuristic policies from the relaxations’ dual prices in a similar fashion to dynamic resource prices used in network revenue management. We finally present a computational study to demonstrate the empirical quality of the new relaxations and policies. Summary of Contribution: Online bipartite matching (OBM) is one of the fundamental problems in the area of online decision analysis with a wide variety of applications in operations research and computer science, for example, online advertising, ride sharing, and general resource allocation. Over the last decades, both communities have been interested in the design and analysis of new approaches. Our main contribution is to provide a polyhedral study that considers the problem’s sequential nature. Specifically, we achieve this via dynamic relaxations. We also discuss how to derive heuristic policies from the relaxations’ dual prices. We support our theoretical findings with a detailed computational study.

Suggested Citation

  • Alfredo Torrico & Alejandro Toriello, 2022. "Dynamic Relaxations for Online Bipartite Matching," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 1871-1884, July.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:4:p:1871-1884
    DOI: 10.1287/ijoc.2022.1168
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    References listed on IDEAS

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    1. Alan S. Manne, 1960. "Linear Programming and Sequential Decisions," Management Science, INFORMS, vol. 6(3), pages 259-267, April.
    2. Patrick Jaillet & Xin Lu, 2014. "Online Stochastic Matching: New Algorithms with Better Bounds," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 624-646, August.
    3. Kalyan Talluri & Garrett van Ryzin, 1998. "An Analysis of Bid-Price Controls for Network Revenue Management," Management Science, INFORMS, vol. 44(11-Part-1), pages 1577-1593, November.
    4. E. G. Coffman & I. Mitrani, 1980. "A Characterization of Waiting Time Performance Realizable by Single-Server Queues," Operations Research, INFORMS, vol. 28(3-part-ii), pages 810-821, June.
    5. Dan Zhang & Daniel Adelman, 2009. "An Approximate Dynamic Programming Approach to Network Revenue Management with Customer Choice," Transportation Science, INFORMS, vol. 43(3), pages 381-394, August.
    6. Chaoxu Tong & Huseyin Topaloglu, 2014. "On the Approximate Linear Programming Approach for Network Revenue Management Problems," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 121-134, February.
    7. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    8. Daniel Adelman, 2007. "Dynamic Bid Prices in Revenue Management," Operations Research, INFORMS, vol. 55(4), pages 647-661, August.
    9. Thomas W. M. Vossen & Dan Zhang, 2015. "Reductions of Approximate Linear Programs for Network Revenue Management," Operations Research, INFORMS, vol. 63(6), pages 1352-1371, December.
    10. Dimitris Bertsimas & José Niño-Mora, 1996. "Conservation Laws, Extended Polymatroids and Multiarmed Bandit Problems; A Polyhedral Approach to Indexable Systems," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 257-306, May.
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