INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.82, no.5, pp.609-616, 2005 (SCI-Expanded)
In this study a minimum cost network flow problem with m + n + 2 nodes and mn arcs, which is equivalent to the transportation problem with m sources and n destinations, is described as an axial four-index transportation problem of order 1 x m x n x 1. Several algebraic characterizations of this problem of order 1 x m x n x 1 are investigated using the singular value decomposition and generalized inverses of its coefficient matrix. The results are compared with some results on the planar four-index transportation problem [5]. It is shown that these problems have common algebraic characterizations and can be solved in terms of eigenvectors of the matrices J(m) and J(n) where J(m) is an m x m matrix, all of whose entries are 1.