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Abstract
In this study, we describe an axial four-index transportation problem of order 1 × m × n × 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 × m × n × 1. It is shown that these problems have common algebraic characterizations, and can be solved in terms of eigenvectors of the matrices Jm and Jn , where Jm is an m × m matrix whose entries are 1.