Abstract
We propose to give a computationally feasible procedure for the generation of all the integer points satisfying a given set of inequalities. Five different systems of inequalities will be considered. In order to generate all of these integer points, one requires a particular set of integer points, called fundamental points, and a set of linearly independent vectors with integer components. The number of these fundamental points is given by a simple formula. We show how to generate the fundamental points and the required vectors. We give an application concerning the localization of the integer optimum of a linear objective function subject to constraints which geometrically define a cone or a parallelotope.
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Fiorot, J.C. Generation of all integer points for given sets of linear inequalities. Mathematical Programming 3, 276–295 (1972). https://doi.org/10.1007/BF01585001
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DOI: https://doi.org/10.1007/BF01585001