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Generating facets for finite master cyclic group polyhedra using n-step mixed integer rounding functions

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  • Kianfar, Kiavash
  • Fathi, Yahya

Abstract

The n-step mixed integer rounding (MIR) functions generate n-step MIR inequalities for MIP problems and are facets for the infinite group problems. We show that the n-step MIR functions also directly generate facets for the finite master cyclic group polyhedra especially in many cases where the breakpoints of the n-step MIR function are not necessarily at the elements of the group (hence the linear interpolation of the facet coefficients obtained has more than two slopes).

Suggested Citation

  • Kianfar, Kiavash & Fathi, Yahya, 2010. "Generating facets for finite master cyclic group polyhedra using n-step mixed integer rounding functions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 105-109, November.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:105-109
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    References listed on IDEAS

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    1. MARCHAND, Hugues & WOLSEY, Laurence A., 2001. "Aggregation and mixed integer rounding to solve mips," LIDAM Reprints CORE 1513, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Hugues Marchand & Laurence A. Wolsey, 2001. "Aggregation and Mixed Integer Rounding to Solve MIPs," Operations Research, INFORMS, vol. 49(3), pages 363-371, June.
    3. Klabjan, Diego, 2007. "Subadditive approaches in integer programming," European Journal of Operational Research, Elsevier, vol. 183(2), pages 525-545, December.
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    Cited by:

    1. Shlyk, Vladimir A., 2013. "Master corner polyhedron: Vertices," European Journal of Operational Research, Elsevier, vol. 226(2), pages 203-210.
    2. 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.

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