THE FORMULATION AND EQUIVALENT CHARACTERIZATIONS OF THE PLANAR THREE INDEX TRANSPORTATION PROBLEM

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

DÜZLEMSEL ÜÇ İNDİSLİ DAĞITIM PROBLEMİNİN FORMÜLASYONU VE EŞDEĞER ÖZELLİKLERİ

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

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3. Bulut H. (1991): “Algebriac Characterizations of the Singular Value Decompositions in the Transportation problem”, J. Math. Anal. Appl., 154, 13-21.
4. Bulut S.A. (1998): “Construction and Algebraic Characterizations of the Planar and Axial Transportation Problems, J. Math. Anal. Appl., 220, 535-552.
5. Graybill F.A. (1969): “Introduction to matrices with applications in statistics”, Wadsworth, Belmont, Calif.
6. Korsnikov A.D., Burkard R.E. (1989): “On the Dimension of Polytopes of Planar Three- Index Transportation Problems, Optimization 20, 1 , 107-116.
7. 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