| Abstract: | 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?×?m?×?n?×?1. Construction and several algebraic characterizations of the planar four-index transportation problem of order 1?×?m?×?n?×?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?×?m matrix whose entries are 1. |
