Mathematical Programming

, Volume 91, Issue 2, pp 391–397

On the rank of mixed 0,1 polyhedra

  • Gérard Cornuéjols
  • Yanjun Li

DOI: 10.1007/s101070100250

Cite this article as:
Cornuéjols, G. & Li, Y. Math. Program. (2002) 91: 391. doi:10.1007/s101070100250


For a polytope in the [0,1]n cube, Eisenbrand and Schulz showed recently that the maximum Chvátal rank is bounded above by O(n2logn) and bounded below by (1+ε)n for some ε>0. Chvátal cuts are equivalent to Gomory fractional cuts, which are themselves dominated by Gomory mixed integer cuts. What do these upper and lower bounds become when the rank is defined relative to Gomory mixed integer cuts? An upper bound of n follows from existing results in the literature. In this note, we show that the lower bound is also equal to n. This result still holds for mixed 0,1 polyhedra with n binary variables.

Key words: mixed integer cut – disjunctive cut – split cut – rank – mixed 0,1 program 
Mathematics Subject Classification (2000): 90C10, 90C11 

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Gérard Cornuéjols
    • 1
  • Yanjun Li
    • 1
  1. 1.Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, USA, e-mail: gc0v@andrew.cmu.eduUS