An axial four-index transportation problem and its algebraic characterizations

Bulut S., Bulut H.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.81, no.6, pp.765-773, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 81 Issue: 6
  • Publication Date: 2004
  • Doi Number: 10.1080/00207160410001708832
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.765-773
  • Keywords: transportation problem, axial four-index transportation problem, circularization network flow problem, NETWORK FLOW PROBLEM, DECOMPOSITIONS, CONSTRUCTION, PLANAR, MATRIX
  • Dokuz Eylül University Affiliated: No

Abstract

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