Abstract
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.
References
- 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
Abstract
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
References
- 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
Details
| Other ID | JA29RK85ZN |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | May 1, 2001 |
| Published in Issue | Year 2001 Volume: 3 Issue: 2 |
Cite
Dokuz Eylül Üniversitesi, Mühendislik Fakültesi Dekanlığı Tınaztepe Yerleşkesi, Adatepe Mah. Doğuş Cad. No: 207-I / 35390 Buca-İZMİR.