Çokamaçlı Kesirli Programlama Problemleri için Q- Taylor Metodu

Bu çalışmada, çok amaçlı lineer kesirli programlama problemlerinin (ÇALKPP) çözümleri için uygun bölgedeki herbir kesirli amaç fonksiyonunun optimal noktalarında amaç fonksiyonlarının birinci dereceden q -Taylor seri açılımları sunulmuştur. Q-Analizde, q - Taylor serisi q -Türevlerine göre bir fonksiyonun q -Serisine genişlemesidir. ÇALKPP problemi, kendisine denk olan çok amaçlı lineer programlama problemlerini (ÇALPP) problemine indirgendi. Amaç fonksiyonlarının ağırlıklarının eşit olduğu kabulü altında ÇALPP çözüldü. Böylece problem tek amaca indirgenmiş oldu. Sunulan metot ile elde edilen çözümler etkin çözümlerdir. Bu sayede ÇALPP problemlerinin çözümündeki karmaşıklık giderilmiş olundu ve sunulan metodun etkinliğini göstermek için bir problem üzerinde uygulanması yapıldı.

Q-Taylor Method for Multiobjective Fractional Programming ProblemQ-Taylor Method for Multiobjective Fractional Programming ProblemQ-Taylor Method for Multiobjective Fractional Programming ProblemQ-Taylor Method for Multiobjective Fractional Programming ProblemQ-Taylor Method for Multiobjective Fract

In this work, we have proposed a solution to Multi Objective Lineer Fractional Programming Problem (MOLFPP) by using the firstorder q-Taylor expansion of these objective functions at optimal points of each fractional objective functions in feasible region. In qcalculus, q-Taylor series is a q-series expansion of a function with respect to q-derivatives. MOFPP reduces to an equivalent MultiObjective Linear Programming Problem (MOLPP). The resulting MOLPP is solved assuming that weights of these objective functionsare equal and considering the sum of the these objective functions. Thus, the problem is reduced to a single objective. The proposedsolution to MOFPP always yields efficient solution. Therefore, the complexity in solving MOFPP has reduced and to show the efficiencyof the q-Taylor series method, we applied the method to a problem.

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