Two-step MIR inequalities for mixed integer programs

Sanjeeb Dash, Marcos Goycoolea, Oktay Günlük

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Two-step mixed integer rounding (MIR) inequalities are valid inequalities derived from a facet of a simple mixed integer set with three variables and one constraint. In this paper we investigate how to effectively use these inequalities as cutting planes for general mixed integer problems. We study the separation problem for single-constraint sets and show that it can be solved in polynomial time when the resulting inequality is required to be sufficiently different from the associated MIR inequalities. We discuss computational issues and present numerical results based on a number of data sets.

Original languageEnglish
Pages (from-to)236-249
Number of pages14
JournalINFORMS Journal on Computing
Issue number2
StatePublished - Mar 2010
Externally publishedYes


  • GMI cut
  • Group polyhedron
  • Mixed integer rounding
  • Separation
  • Two-step MIR


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