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Facets of the knapsack polytope

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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.

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References

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This paper was first circulated under [1]. A brief note on it was published under [2].

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Balas, E. Facets of the knapsack polytope. Mathematical Programming 8, 146–164 (1975). https://doi.org/10.1007/BF01580440

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  • DOI: https://doi.org/10.1007/BF01580440

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