Construction and algebraic characterizations of a planar four-index transportation problem equivalent to a circularization network flow problem

Author： Bulut H. Bulut S.A.

Publisher： Taylor & Francis Ltd

ISSN： 0020-7160

Source： International Journal of Computer Mathematics, Vol.80, Iss.11, 2003-11, pp. : 1373-1383

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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.