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New inequalities for finite and infinite group problems from approximate lifting

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  • 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
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    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.
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    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.

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