Some properties of transportation manifold

In this paper it is shown that the set of equality constraints of transportation problem can be represented as an intersection of two orthogonal affine sets. Projection point onto transportation manifold then could be achieved by consecutive projections onto these sets using simple formulas. This result can be used in solving a linear transportaiotn problem (in variant of Karmarkar projective algorithm), as well as in a nonlinear case (by gradient projection method).