Abstract
The permutahedron of a poset is the convex hull of all incidence vectors of linear extensions. For the case ofN-sparse posets in which any five elements induce at most oneN we give a characterization of the permutahedron in terms of linear inequalities. This yields an LP-solution for minimizing the weighted mean completion time for jobs with unit processing times andN-sparse precedence constraints. We close with an extension of our approach to arbitrary processing times.
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von Arnim, A., Schrader, R. & Wang, Y. The permutahedron ofN-sparse posets. Mathematical Programming 75, 1–18 (1996). https://doi.org/10.1007/BF02592204
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DOI: https://doi.org/10.1007/BF02592204