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CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions

Author

Listed:
  • Tuomas Sandholm

    () (Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Subhash Suri

    () (Department of Computer Science, University of California, Santa Barbara, California 93106)

  • Andrew Gilpin

    () (CombineNet, Inc., Fifteen 27th Street, Pittsburgh, Pennsylvania 15222)

  • David Levine

    () (CombineNet, Inc., Fifteen 27th Street, Pittsburgh, Pennsylvania 15222)

Abstract

Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is \scr{N}\scr{P}-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster---especially in cases with structure. CABOB's search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem---the run-time distribution does not have a heavy tail.

Suggested Citation

  • Tuomas Sandholm & Subhash Suri & Andrew Gilpin & David Levine, 2005. "CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions," Management Science, INFORMS, vol. 51(3), pages 374-390, March.
  • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:3:p:374-390
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    File URL: http://dx.doi.org/10.1287/mnsc.1040.0336
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    References listed on IDEAS

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    Cited by:

    1. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2007. "Column aggregation-based pricing combinatorial auctions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 624, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2007. "Non-linear anonymous pricing combinatorial auctions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 625, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Drexl, Andreas & Jörnsten, Kurt & Knof, Diether, 2005. "Non-linear anonymous pricing in combinatorial auctions," Discussion Papers 2005/6, Norwegian School of Economics, Department of Business and Management Science.
    4. repec:pal:jorsoc:v:58:y:2007:i:12:d:10.1057_palgrave.jors.2602299 is not listed on IDEAS
    5. Rancourt, Marie-Ève & Bellavance, François & Goentzel, Jarrod, 2014. "Market analysis and transportation procurement for food aid in Ethiopia," Socio-Economic Planning Sciences, Elsevier, vol. 48(3), pages 198-219.
    6. G. Anandalingam & Robert W. Day & S. Raghavan, 2005. "The Landscape of Electronic Market Design," Management Science, INFORMS, vol. 51(3), pages 316-327, March.
    7. Schnizler, Bjorn & Neumann, Dirk & Veit, Daniel & Weinhardt, Christof, 2008. "Trading grid services - a multi-attribute combinatorial approach," European Journal of Operational Research, Elsevier, vol. 187(3), pages 943-961, June.
    8. Stößer, Jochen & Neumann, Dirk & Weinhardt, Christof, 2010. "Market-based pricing in grids: On strategic manipulation and computational cost," European Journal of Operational Research, Elsevier, vol. 203(2), pages 464-475, June.
    9. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2005. "Non-linear anonymous pricing in combinatorial auctions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 598, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    10. repec:spr:annopr:v:245:y:2016:i:1:d:10.1007_s10479-014-1669-4 is not listed on IDEAS
    11. Gediminas Adomavicius & Shawn P. Curley & Alok Gupta & Pallab Sanyal, 2012. "Effect of Information Feedback on Bidder Behavior in Continuous Combinatorial Auctions," Management Science, INFORMS, vol. 58(4), pages 811-830, April.
    12. Alidaee, Bahram & Kochenberger, Gary & Lewis, Karen & Lewis, Mark & Wang, Haibo, 2008. "A new approach for modeling and solving set packing problems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 504-512, April.
    13. repec:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-014-1776-2 is not listed on IDEAS
    14. Chang, Tsung-Sheng, 2009. "Decision support for truckload carriers in one-shot combinatorial auctions," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 522-541, June.
    15. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2009. "Non-linear anonymous pricing combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 296-302, November.
    16. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.
    17. Ervasti, Valtteri & Leskelä, Riikka-Leena, 2010. "Allocative efficiency in simulated multiple-unit combinatorial auctions with quantity support," European Journal of Operational Research, Elsevier, vol. 203(1), pages 251-260, May.

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