INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.80, no.11, pp.1373-1383, 2003 (SCI-Expanded)
In this study, a circularization network flow problem with m + n + 2 nodes and (m + 1)(n + 1) arcs is described as a planar four-index transportation problem of order 1 x m x n x 1. Construction and several algebraic characterizations of the planar four-index transportation problem of order 1 x m x n x 1 are investigated using the generalized inverse and singular value decomposition of its coefficient matrix. The results are compared with some results we obtained on the transportation problem with m sources and n destinations. It is shown that these problems can be solved in terms of eigenvectors of the matrices J(m) and J(n), where J(m) is a m x m matrix whose entries are 1.