FUZZY MULTI-OBJECTIVE NONLINEAR PROGRAMMING PROBLEMS UNDER VARİOUS MEMBERSHIP FUNCTIONS: A COMPARATİVE ANALYSIS

Abstract

Fuzzy sets have been applied to various decision-making problems when there is uncertainty in real-life problems. In decision-making problems, objective functions and constraints sometimes cannot be expressed linearly. In such cases, the problems discussed are expressed by nonlinear programming models. Fuzzy multi-objective programming models are problems containing multiple objective functions, where objective functions and/or constraints include fuzzy parameters. Membership functions are crucial to obtain optimal solution of fuzzy multi-objective programming model. In this study, a green supply chain network model with fuzzy parameters is proposed. Proposed model with nonlinear constraints is a fuzzy multi-objective nonlinear programming model that minimizes both transportation costs and emissions generated by two vehicle types during transportation. The model is used in Zimmermann's Min-Max approach by considering triangular, hyperbolic and exponential membership functions and optimal solutions are obtained. When optimal solutions are compared, it is seen that optimal solution obtained using the hyperbolic membership function is better than the optimal solutions obtained from triangular and exponential ones. Maximum common satisfaction level calculated using hyperbolic membership function for proposed model is λ=0.97. Sensitivity analysis is also carried out by taking into account distances between suppliers, manufacturers, distribution centers and customers, as well as customer demands.

Keywords

• Green Supply Chain
• Fuzzy Multi-objective Nonlinear Programming
• Fuzzy Multi-objective Programming
• Fuzzy Sets
• Membership Functions
• Zimmermann’s Min-Max Approach

ÇEŞITLI ÜYELIK FONKSIYONLARI ALTINDA BULANIK ÇOK AMAÇLI DOĞRUSAL OLMAYAN PROGRAMLAMA PROBLEMLERİ: KARŞILAŞTIRMALI BIR ANALİZ

Abstract

Bulanık kümeler, gerçek hayat problemlerinde belirsizlik olması durumunda çeşitli karar verme problemlerine uygulanmaktadır. Karar verme problemlerinde amaç fonksiyonları ve kısıtlar bazen doğrusal olarak ifade edilemez. Bu gibi durumlarda, ele alınan problemler doğrusal olmayan programlama modelleri ile ifade edilir. Bulanık çok amaçlı programlama modelleri, amaç fonksiyonları ve/veya kısıtların bulanık terimler içerdiği birden fazla amaç fonksiyonu olan problemlerdir. Bulanık çok amaçlı programlama modellerinin çözümünde kullanılan üyelik fonksiyonları, karar verme aşamasında çok önemlidir. Bu çalışmada, bulanık parametrelere sahip bir yeşil tedarik zinciri ağı modeli önerilmiştir. Doğrusal olmayan kısıtları olan model, hem taşıma maliyetlerini hem de taşıma esnasında iki araç tipi tarafından üretilen emisyonları en aza indiren bulanık çok amaçlı doğrusal olmayan programlama modelidir. Model, üçgensel, hiperbolik ve üstel üyelik fonksiyonları gözönüne alınarak Zimmermann'ın Min-Max yaklaşımında kullanılmış ve optimal çözümler elde edilmiştir. Optimal çözümler karşılaştırıldığında, hiperbolik üyelik fonksiyonu kullanılarak elde edilen optimal çözümün üçgensel ve üstel üyelik fonksiyonlarından elde edilen optimal çözümlerden daha iyi olduğu görülmüştür. Önerilen model için hiperbolik üyelik fonksiyonu kullanılarak hesaplanan maksimum ortak memnuniyet düzeyi λ=0.97’dir. Çalışmada, müşteri taleplerinin yanı sıra tedarikçiler, üreticiler, dağıtım merkezleri ve müşteriler arasındaki mesafeler dikkate alınarak duyarlılık analizi de yapılmıştır.

Keywords

• Yeşil Tedarik Zinciri
• Bulanık Çok Amaçlı Doğrusal Olmayan Programlama
• Bulanık Çok Amaçlı Programlama
• Bulanık Kümeler
• Üyelik Fonksiyonları
• Zimmermann

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