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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
    DOI: 10.1287/mnsc.1040.0336
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    References listed on IDEAS

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    5. Abhishek Ray & Mario Ventresca & Karthik Kannan, 2021. "A Graph-Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions," Information Systems Research, INFORMS, vol. 32(4), pages 1099-1114, December.
    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. 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.
    8. Gülşah Karakaya & Murat Köksalan, 2016. "An interactive approach for Bi-attribute multi-item auctions," Annals of Operations Research, Springer, vol. 245(1), pages 97-119, October.
    9. 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.
    10. A Drexl & K Jørnsten, 2007. "Reflections about pseudo-dual prices in combinatorial auctions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1652-1659, December.
    11. Yunpeng Pan & Zhe Liang, 2017. "Dual relaxations of the time-indexed ILP formulation for min–sum scheduling problems," Annals of Operations Research, Springer, vol. 249(1), pages 197-213, February.
    12. 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.
    13. 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.
    14. 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.
    15. Robert W. Day & S. Raghavan, 2009. "Matrix Bidding in Combinatorial Auctions," Operations Research, INFORMS, vol. 57(4), pages 916-933, August.
    16. 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.
    17. Dries R. Goossens & Rudolf Müller & Frits C. R. Spieksma, 2010. "Algorithms for Recognizing Economic Properties in Matrix Bid Combinatorial Auctions," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 339-352, August.
    18. Richard Li-Yang Chen & Shervin AhmadBeygi & Amy Cohn & Damian R. Beil & Amitabh Sinha, 2009. "Solving Truckload Procurement Auctions Over an Exponential Number of Bundles," Transportation Science, INFORMS, vol. 43(4), pages 493-510, November.
    19. 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.
    20. Mercedes Landete & Juan Monge & Antonio Rodríguez-Chía, 2013. "Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem," Annals of Operations Research, Springer, vol. 207(1), pages 137-160, August.
    21. 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.
    22. Tuomas Sandholm & David Levine & Michael Concordia & Paul Martyn & Rick Hughes & Jim Jacobs & Dennis Begg, 2006. "Changing the Game in Strategic Sourcing at Procter & Gamble: Expressive Competition Enabled by Optimization," Interfaces, INFORMS, vol. 36(1), pages 55-68, February.
    23. Gediminas Adomavicius & Alok Gupta & Mochen Yang, 2022. "Bidder Support in Multi-item Multi-unit Continuous Combinatorial Auctions: A Unifying Theoretical Framework," Information Systems Research, INFORMS, vol. 33(4), pages 1174-1195, December.
    24. Jawad Abrache & Teodor Crainic & Michel Gendreau & Monia Rekik, 2007. "Combinatorial auctions," Annals of Operations Research, Springer, vol. 153(1), pages 131-164, September.

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