Linear Integer Programming.
NAVAL RESEARCH LAB WASHINGTON D C MATHEMATICS RESEARCH CENTER
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Some of the mathematical aspects of the group theoretic approach to linear integer programs were analyzed. The manner in which an Abelian group is associated with a linear integer program has been analyzed. Corresponding to each linear integer program is an associated polyhedron. The geometric structure of this polyhedron reflects the structure of the linear integer program. If the polyedron is known, then under appropriate conditions the optimal solution of the integer program is known. Some properties of these Abelian polyhedra, associated with Abelian groups, are discussed. A computer implementation of the group theoretic approach is included in the report.
- Operations Research