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Algebraic and Combinatorial Methods in Operations Research: Workshop Proceedings (Mathematics Studies)
Algebraic and Combinatorial Methods in Operations Research: Workshop Proceedings (Mathematics Studies)
Date: 11 April 2011, 18:11

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We define an optimization problem in the discrete semimodule over the natural numbers given by an ordered commutative semigroup and show that a canonical order induced in any semigroup by the right-hand-side element give an ordered semigroup for which the optimization problem is equivalent to the (Equality) Semigroup Program, therefore the extension is consistent. Packing Programs correspond to positively ordered semigroups satisfying a self-positive condition, in these cases the semimodule is ordered. Packing Programs give a generalization of Integer Packing Programs. We show that the facets of the convex hull of solutions to a Packing Program are super-additives and we characterize the polars and neopolars of Master Packing Programs.

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