INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.81, no.6, pp.765-773, 2004 (SCI-Expanded)
In this study, we describe an axial four-index transportation problem of order 1 x m x n x 1, which is equivalent to a circularization network flow problem with m + n + 2 nodes and ( m + 1)( n + 1) arcs. We then give some algebraic characterizations of the axial four-index transportation problem, and compare the results we obtained with some results on the planar four-index transportation problem of order 1 x m x n x 1. 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 whose entries are 1.