Mathematical Programming

, Volume 8, Issue 1, pp 146–164 | Cite as

Facets of the knapsack polytope

  • Egon Balas


A necessary and sufficient condition is given for an inequality with coefficients 0 or 1 to define a facet of the knapsack polytope, i.e., of the convex hull of 0–1 points satisfying a given linear inequality. A sufficient condition is also established for a larger class of inequalities (with coefficients not restricted to 0 and 1) to define a facet for the same polytope, and a procedure is given for generating all facets in the above two classes. The procedure can be viewed as a way of generating cutting planes for 0–1 programs.


Hull Mathematical Method Convex Hull Large Class Linear Inequality 
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Copyright information

© The Mathematical Programming Society 1975

Authors and Affiliations

  • Egon Balas
    • 1
  1. 1.Carnegie-Mellon UniversityPittsburghUSA

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