IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v55y2008i2p172-191.html
   My bibliography  Save this article

New inequalities for finite and infinite group problems from approximate lifting

Author

Listed:
  • Lisa A. Miller
  • Yanjun Li
  • Jean‐Philippe P. Richard

Abstract

In this paper, we derive new families of facet‐defining inequalities for the finite group problem and extreme inequalities for the infinite group problem using approximate lifting. The new valid inequalities for the finite group problem include two‐ and three‐slope facet‐defining inequalities as well as the first family of four‐slope facet‐defining inequalities. The new valid inequalities for the infinite group problem include families of two‐ and three‐slope extreme inequalities. These new inequalities not only illustrate the diversity of strong inequalities for the finite and infinite group problems, but also provide a large variety of new cutting planes for solving integer and mixed‐integer programming problems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Suggested Citation

  • Lisa A. Miller & Yanjun Li & Jean‐Philippe P. Richard, 2008. "New inequalities for finite and infinite group problems from approximate lifting," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 172-191, March.
    • Handle: RePEc:wly:navres:v:55:y:2008:i:2:p:172-191
    DOI: 10.1002/nav.20275
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20275
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20275?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
    ---><---

    References listed on IDEAS

    as
    1. LOUVEAUX, Quentin & WOLSEY, Laurence A., 2003. "Lifting, superadditivity, mixed integer rounding and single node flow sets revisited," LIDAM Reprints CORE 1659, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Zonghao Gu & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Sequence Independent Lifting in Mixed Integer Programming," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 109-129, March.
    3. LOUVEAUX, Quentin & WOLSEY, Laurence, 2003. "Lifting, superadditivity, mixed integer rounding and single node flow sets revisited," LIDAM Discussion Papers CORE 2003001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Gérard Cornuéjols & Yanjun Li & Dieter Vandenbussche, 2003. "K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 385-396, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amitabh Basu & Robert Hildebrand & Matthias Köppe, 2015. "Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. I. The One-Dimensional Case," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 105-129, February.
    2. Amitabh Basu & Michele Conforti & Marco Di Summa & Joseph Paat, 2019. "The Structure of the Infinite Models in Integer ProgrammingAbstract: The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces ," Management Science, INFORMS, vol. 44(4), pages 1412-1430, November.

    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. Yves Crama & Michel Grabisch & Silvano Martello, 2022. "Sixty-one surveys in operations research," Annals of Operations Research, Springer, vol. 314(1), pages 5-13, July.
    2. Quentin Louveaux & Laurence Wolsey, 2007. "Lifting, superadditivity, mixed integer rounding and single node flow sets revisited," Annals of Operations Research, Springer, vol. 153(1), pages 47-77, September.
    3. Denis Bouyssou & Silvano Martello & Frank Plastria, 2010. "Eleven surveys in operations research: II," Annals of Operations Research, Springer, vol. 175(1), pages 3-8, March.
    4. Leo Liberti & Thierry Marchant & Silvano Martello, 2013. "Eleven surveys in operations research: III," Annals of Operations Research, Springer, vol. 204(1), pages 3-9, April.
    5. Yves Crama & Michel Grabisch & Silvano Martello, 2018. "Surveys in operations research," Annals of Operations Research, Springer, vol. 271(1), pages 3-10, December.
    6. Leo Liberti & Thierry Marchant & Silvano Martello, 2016. "Twelve surveys in operations research," Annals of Operations Research, Springer, vol. 240(1), pages 3-11, May.
    7. Alper Atamtürk, 2005. "Cover and Pack Inequalities for (Mixed) Integer Programming," Annals of Operations Research, Springer, vol. 139(1), pages 21-38, October.
    8. Avella, P. & Boccia, M. & Mattia, S. & Rossi, F., 2021. "Weak flow cover inequalities for the capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 289(2), pages 485-494.
    9. Agra, Agostinho & Constantino, Miguel Fragoso, 2016. "Lifted Euclidean inequalities for the integer single node flow set with upper bounds," European Journal of Operational Research, Elsevier, vol. 251(1), pages 53-63.
    10. Alper Atamtürk, 2004. "Sequence Independent Lifting for Mixed-Integer Programming," Operations Research, INFORMS, vol. 52(3), pages 487-490, June.
    11. Akbalik, A. & Pochet, Y., 2009. "Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs," European Journal of Operational Research, Elsevier, vol. 198(2), pages 412-434, October.
    12. William Cook & Sanjeeb Dash & Ricardo Fukasawa & Marcos Goycoolea, 2009. "Numerically Safe Gomory Mixed-Integer Cuts," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 641-649, November.
    13. Kaparis, Konstantinos & Letchford, Adam N., 2008. "Local and global lifted cover inequalities for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 91-103, April.
    14. Atamturk, Alper & Munoz, Juan Carlos, 2002. "A Study of the Lot-Sizing Polytope," University of California Transportation Center, Working Papers qt6zz2g0z4, University of California Transportation Center.
    15. Miller, Andrew J. & Nemhauser, George L. & Savelsbergh, Martin W. P., 2000. "On the capacitated lot-sizing and continuous 0-1 knapsack polyhedra," European Journal of Operational Research, Elsevier, vol. 125(2), pages 298-315, September.
    16. Yang, Zhen & Chen, Haoxun & Chu, Feng & Wang, Nengmin, 2019. "An effective hybrid approach to the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 467-480.
    17. Michele Conforti & Gérard Cornuéjols & Giacomo Zambelli, 2011. "A Geometric Perspective on Lifting," Operations Research, INFORMS, vol. 59(3), pages 569-577, June.
    18. Agostinho Agra & Cristina Requejo & Eulália Santos, 2016. "Implicit cover inequalities," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1111-1129, April.
    19. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    20. Yongjia Song & James R. Luedtke & Simge Küçükyavuz, 2014. "Chance-Constrained Binary Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 735-747, November.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:55:y:2008:i:2:p:172-191. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.