Öz
In this paper, we investigate the equivalent formulations of the planar three index
transportation problem, of order mxnxp, using the generalized inverse of its coefficient
matrix, and give relations between the equivalent problems. It is then shown that the problem
and its equivalent problems have common algebraic characterizations.
Anahtar Kelimeler
Transportation problem Linear programming problem Generalized inverses
Kaynakça
- Ben-Israel A., Grenville T.N.E. (1974): “Generalized inverses: theory and applications”, J.Wiley, New York.
- Brewer J.M. (1978): “Kronecker Products and Matrix Calculus in System Theory”, IEEE Tran. on Circuits and Systems, Vol cas-25, no.9, 772-781.
- Bulut H. (1991): “Algebriac Characterizations of the Singular Value Decompositions in the Transportation problem”, J. Math. Anal. Appl., 154, 13-21.
- Bulut S.A. (1998): “Construction and Algebraic Characterizations of the Planar and Axial Transportation Problems, J. Math. Anal. Appl., 220, 535-552.
- Graybill F.A. (1969): “Introduction to matrices with applications in statistics”, Wadsworth, Belmont, Calif.
- Korsnikov A.D., Burkard R.E. (1989): “On the Dimension of Polytopes of Planar Three- Index Transportation Problems, Optimization 20, 1 , 107-116.
- Vlach M. (1986): “Conditions for the Existence of Solutions of the Three-Dimensional Planar Transportation Problem, Discrete Applied Mathematics 13, 61-78. (21) β,x≥0 x |(JJp⊗J n ⊗J m)x =pnmA + Minc
Öz
Bu çalışmada, m çıkışlı, n depolu ve p varışlı düzlemsel üç indisli dağıtım probleminin
formülasyonu ve eşdeğer formülasyonları incelenmiştir. Problem ve eşdeğer problemlerin
cebirsel özellikleri, katsayılar matrisinin genelleştirilmiş tersleri kullanılarak verilmiştir.
Problem ve eşdeğer problemlerin ortak cebirsel özelliklere sahip oldukları görülmüştür
Anahtar Kelimeler
Dağıtım problemi Doğrusal programlama problemi Genelleştirilmiş tersler
Kaynakça
- Ben-Israel A., Grenville T.N.E. (1974): “Generalized inverses: theory and applications”, J.Wiley, New York.
- Brewer J.M. (1978): “Kronecker Products and Matrix Calculus in System Theory”, IEEE Tran. on Circuits and Systems, Vol cas-25, no.9, 772-781.
- Bulut H. (1991): “Algebriac Characterizations of the Singular Value Decompositions in the Transportation problem”, J. Math. Anal. Appl., 154, 13-21.
- Bulut S.A. (1998): “Construction and Algebraic Characterizations of the Planar and Axial Transportation Problems, J. Math. Anal. Appl., 220, 535-552.
- Graybill F.A. (1969): “Introduction to matrices with applications in statistics”, Wadsworth, Belmont, Calif.
- Korsnikov A.D., Burkard R.E. (1989): “On the Dimension of Polytopes of Planar Three- Index Transportation Problems, Optimization 20, 1 , 107-116.
- Vlach M. (1986): “Conditions for the Existence of Solutions of the Three-Dimensional Planar Transportation Problem, Discrete Applied Mathematics 13, 61-78. (21) β,x≥0 x |(JJp⊗J n ⊗J m)x =pnmA + Minc
Ayrıntılar
| Diğer ID | JA29RK85ZN |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 1 Mayıs 2001 |
| Yayımlandığı Sayı | Yıl 2001 Cilt: 3 Sayı: 2 |
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