IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v207y2013i1p137-16010.1007-s10479-011-1039-4.html
   My bibliography  Save this article

Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem

Author

Listed:
  • Mercedes Landete
  • Juan Monge
  • Antonio Rodríguez-Chía

Abstract

An alternative formulation for the set packing problem in a higher dimension is presented. The addition of a new family of binary variables allows us to find new valid inequalities, some of which are shown to be facets of the polytope in the higher dimension. We also consider the Winner Determination Problem, which is equivalent to the set packing problem and whose special structure allows us to easily implement these valid inequalities in a very easy way. The computational experiments illustrate the performance of the valid inequalities and obtain good results. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:207:y:2013:i:1:p:137-160:10.1007/s10479-011-1039-4
    DOI: 10.1007/s10479-011-1039-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-1039-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-1039-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Juan Aparicio & Mercedes Landete & Juan Monge & Inmaculada Sirvent, 2008. "A new pricing scheme based on DEA for iterative multi-unit combinatorial auctions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 319-344, December.
    2. Aleksandar Pekev{c} & Michael H. Rothkopf, 2003. "Combinatorial Auction Design," Management Science, INFORMS, vol. 49(11), pages 1485-1503, November.
    3. Hanif D. Sherali & Warren P. Adams & Patrick J. Driscoll, 1998. "Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems," Operations Research, INFORMS, vol. 46(3), pages 396-405, June.
    4. 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.
    5. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    6. Kwon, Roy H., 2005. "Data dependent worst case bounds for weighted set packing," European Journal of Operational Research, Elsevier, vol. 167(1), pages 68-76, November.
    7. Egon Balas & Eitan Zemel, 1977. "Critical Cutsets of Graphs and Canonical Facets of Set-Packing Polytopes," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 15-19, February.
    8. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    9. Laureano Escudero & Araceli Garín & Gloria Pérez, 1999. "On using an automatic scheme for obtaining the convex hull defining inequalities of a Weismantel 0–1 knapsack constraint," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 145-153, June.
    10. I. R. De Farias & E. L. Johnson & G. L. Nemhauser, 2002. "Facets of the Complementarity Knapsack Polytope," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 210-226, February.
    11. 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.
    12. Jawad Abrache & Teodor Crainic & Michel Gendreau & Monia Rekik, 2007. "Combinatorial auctions," Annals of Operations Research, Springer, vol. 153(1), pages 131-164, September.
    13. Rahul Garg & Sanjiv Kapoor, 2006. "Auction Algorithms for Market Equilibrium," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 714-729, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Jawad Abrache & Teodor Crainic & Michel Gendreau & Monia Rekik, 2007. "Combinatorial auctions," Annals of Operations Research, Springer, vol. 153(1), pages 131-164, September.
    4. 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.
    5. Hammami, Farouk & Rekik, Monia & Coelho, Leandro C., 2021. "Exact and hybrid heuristic methods to solve the combinatorial bid construction problem with stochastic prices in truckload transportation services procurement auctions," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 204-229.
    6. Gansterer, Margaretha & Hartl, Richard F. & Sörensen, Kenneth, 2020. "Pushing frontiers in auction-based transport collaborations," Omega, Elsevier, vol. 94(C).
    7. Vangerven, Bart & Goossens, Dries R. & Spieksma, Frits C.R., 2017. "Winner determination in geometrical combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 258(1), pages 254-263.
    8. 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.
    9. 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.
    10. Nguyen, Tri-Dung, 2014. "A fast approximation algorithm for solving the complete set packing problem," European Journal of Operational Research, Elsevier, vol. 237(1), pages 62-70.
    11. G. Anandalingam & Robert W. Day & S. Raghavan, 2005. "The Landscape of Electronic Market Design," Management Science, INFORMS, vol. 51(3), pages 316-327, March.
    12. 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.
    13. 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.
    14. Avenali, Alessandro, 2009. "Exploring the VCG mechanism in combinatorial auctions: The threshold revenue and the threshold-price rule," European Journal of Operational Research, Elsevier, vol. 199(1), pages 262-275, November.
    15. Dries R. Goossens & Sander Onderstal & Jan Pijnacker & Frits C. R. Spieksma, 2014. "Solids: A Combinatorial Auction for Real Estate," Interfaces, INFORMS, vol. 44(4), pages 351-363, August.
    16. 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.
    17. Marcelo Olivares & Gabriel Y. Weintraub & Rafael Epstein & Daniel Yung, 2012. "Combinatorial Auctions for Procurement: An Empirical Study of the Chilean School Meals Auction," Management Science, INFORMS, vol. 58(8), pages 1458-1481, August.
    18. Henry Schellhorn, 2004. "A Double-Sided Multiunit Combinatorial Auction for Substitutes: Theory and Algorithms," FAME Research Paper Series rp123, International Center for Financial Asset Management and Engineering.
    19. Robert W. Day & S. Raghavan, 2009. "Matrix Bidding in Combinatorial Auctions," Operations Research, INFORMS, vol. 57(4), pages 916-933, August.
    20. Rönnqvist, Mikael & D'Amours, Sophie & Carle, Marc-André & Azouzi, Riadh, 2018. "Timber selling policies using bundle-based auction: The case of public forests in Québec," Forest Policy and Economics, Elsevier, vol. 96(C), pages 9-18.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:207:y:2013:i:1:p:137-160:10.1007/s10479-011-1039-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.