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Mathematical Programming

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

Facets of the knapsack polytope

  • Egon Balas
Article

Abstract

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.

Keywords

Hull Mathematical Method Convex Hull Large Class Linear Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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