On the Noninteger Polyhedron Vertices of the Three-index Axial Transportation Problem

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 ∈ l4,6,7,...,d(n, m, k)r, where d(n, m, k) = minln, m + k - 2r + m + k - 2, n ≥ m ≥ k ≥ 3.