Taylor series solution of multi objective linear fractional programming problem

Bu makalede, Çok Amaçlı Doğrusal Kesirli Programlama Probleminin uygun bölgesindeki, her doğrusal kesirli amaç fonksiyonunu optimal yapan noktalarda, kesirli lineer amaç fonksiyonları Taylor serisine açılarak, Çok Amaçlı Doğrusal Kesirli Programlama Problemi, Çok Amaçlı Doğrusal Programlama Problemine dönüştürül-müştür. Daha sonra da, doğrusal amaç fonksiyonlarının ağırlıkları dikkate alınarak, ağırlıklı toplamı bulunmuştur. Ardından, tek amaçlı doğrusal programlama problemi elde edilmiştir. Bu doğrusal programlama probleminin optimal çözümü, çok amaçlı doğrusal kesirli programlama probleminin etkin, hatta, kuvvetli etkin çözümlerini belirlemektedir. Önerilen çözümün etkinliğini göstermek için, örnek uygulamalar yapılmış olup, örneklerin çözümünde WinQSB bilgisayar paket programı kullanılmıştır.

Çok amaçlı doğrusal kesirli programlama probleminin Taylor serisiyle çözümü

In this paper, we have proposed a solution to Multi Objective Linear Fractional Programming Problem (MOLFPP) by expanding the order 1st Taylor polynomial series these objective functions at optimal points of each linear fractional objective functions in feasible region. MOLFPP reduces to an equivalent Multi Objective Linear Programming Problem (MOLPP). The resulting MOLPP is solved assuming that weights of these linear objective functions are equal and considering the sum of the these linear objective functions. The proposed solution to MOLFPP always yields efficient solution, even a strong-efficient solution. Therefore, the complexity in solving MOLFPP has reduced easy computational. To show the ability the proposed solution, three different numerical examples have been presented. The given examples are solved using optimization software WINQSB.(Chang, 2001)

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