INVESTIGATION OF OPTIMALITY CONDITIONS OF THE TRANSPORTATION PROBLEM

Öz

In this study, optimality conditions of the transportation problem with m origins and n destinations have been investigated by using properties of Lagrange functions and Hessian matrix. It is shown that the problem and its reduced cases have common algebraic characterizations.

Anahtar Kelimeler

• Transportation problem, Lagrange function, Hessian matrix

DAĞITIM PROBLEMİNİN OPTİMALLİK KOŞULLARININ İNCELENMESİ

Öz

Bu çalışmada, m çıkış ve n varışlı bir dağıtım probleminin optimallik koşulları, Lagrange fonksiyonu ve Hessian matrisinin özellikleri kullanılarak incelenmiştir. Problemin ve indirgenmiş halinin aynı cebirsel özelliklere sahip olduğu görülmüştür.

Anahtar Kelimeler

• Dağıtım problemi, Lagrange fonksiyonu, Hessian matrisi

Kaynakça

1. Bazaraa M.S., Jarvis J.J., Sherali H.D., (1990): “Linear Programming and Network Flows”, Canada, John Wiley and Sons Inc.
2. Bulut H., (1982): “Bir Ağ Akışı Probleminin Genelleştirilmiş Ters Matrislerle İncelenmesi”, İzmir, Doçentlik Tezi.
3. Bulut H., (1991): “Algebraic Characterizations of the Singular Value Decompositions in the Transportation Problem”, J. Math. Anal. Appl., 154 , 13-21.
4. Bulut H., (1991): “Further Results on the Spectral Decomposition of an Incidence Matrix”, J.Math. Anal. Appl., 158, 466-475.
5. Bulut H., Bulut S.A., (1993): “Spectral Decompositions and Generalized Inverses in a Circularization Network Flow Problem”, J.Math. Anal. Appl., 174, 390-402.
6. Carre B., (1979): “Graph and Networks”, New York, Oxford University Press.
7. Ford L.R., Fulkerson D.R., (1962): “Flows in Networks”, New Jersey, Princeton University Press.
8. Hu T. C., (1970): “Integer Programming and Network Flows”, London, Addison-Wesley.

9. Marlow W.H., (1978): “Mathematics for Operations Research”, New York, John Wiley and Sons Inc.
10. Pyle L.D., (1972): “The Generalized Inverse in Linear Programming Basic Structure”, SIAM J. Appl. Math., 22, pp.335-355.
11. Simonnard M., (1966): “Linear Programming”, New Jersey, Prentice Hall.