Further results on the algebraic characterizations of a minimum cost network flow problem equivalent to the transportation problem
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.82, sa.5, ss.609-616, 2005 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 82 Sayı: 5
- Basım Tarihi: 2005
- Doi Numarası: 10.1080/00207160512331331192
- Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.609-616
- Anahtar Kelimeler: minimum cost network flow problem, transportation problem, singular value decomposition, generalized inverses
- Dokuz Eylül Üniversitesi Adresli: Evet
Özet
In this study a minimum cost network flow problem with m + n + 2 nodes and mn arcs, which is equivalent to the transportation problem with m sources and n destinations, is described as an axial four-index transportation problem of order 1 x m x n x 1. Several algebraic characterizations of this problem of order 1 x m x n x 1 are investigated using the singular value decomposition and generalized inverses of its coefficient matrix. The results are compared with some results on the planar four-index transportation problem [5]. 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, all of whose entries are 1.