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


Bulut H., Bulut S.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.80, no.11, pp.1373-1383, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 80 Issue: 11
  • Publication Date: 2003
  • Doi Number: 10.1080/00207160310001603325
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1373-1383
  • Keywords: transportation problem, planar four-index transportation problem, circularization network flow problem, generalized inverses, singular value decomposition, DECOMPOSITIONS, MATRIX
  • Dokuz Eylül University Affiliated: No

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 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.