Abstract
For the three-index axial transportation polyhedron defined by the integer vector, existence of noninteger vertices was proved. In particular, the three-index n × m × k axial transportation polyhedron having vertices with r fractional components was shown to exist for and only for any number r ∈ {4,6,7,...,δ(n, m, k)}, where δ(n, m, k) = min{n, m + k - 2} + m + k - 2, n ≥ m ≥ k ≥ 3.
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Kravtsov, M.K., Lukshin, E.V. On the Noninteger Polyhedron Vertices of the Three-index Axial Transportation Problem. Automation and Remote Control 65, 422–430 (2004). https://doi.org/10.1023/B:AURC.0000019374.29519.c2
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DOI: https://doi.org/10.1023/B:AURC.0000019374.29519.c2