Fuzzy Goal Programming Problem Based on Minmax Approach for Optimal System Design

Abstract

Every system in nature evolved in order to carry on their existence and reach their targets with minimal losses. The fundamental condition of a system’s success lies on making the correct decision by evaluating multiple, complicated, and conflicting goals based on the present constraints. Many mathematical programming problems are make up of objective functions combined by the decision maker based on the constrains. This study investigates how an optimal design can be reached based on Minmax approach. Goal Programming and a Fuzzy Goal Programming known as MA approach are used in this study. The solution of a problem organized as a Multiple De novo programming in order to determine the resource amounts for a business in handcrafts is carried out based on these two approaches. Budget constrain is organized as a goal to solve the problem based on MA approach, and a solution is proposed accordingly. The acquired results suggest that the solution results of Minmax Goal Programming and MA approach are the same.

Keywords

• De Novo Programming,Fuzzy Goal Programming,Minmax Goal Programming

Optimal Sistem Tasarımı İçin Minmaks Tabanlı Bulanık Hedef Programlama Kullanımı

Öz

Tabiattaki bütün sistemler, varlıklarını devam ettirmek ve hedeflerine en az kayıpla ulaşmak için zaman içerisinde değişim geçirmişlerdir. Sistemlerin başarıya ulaşabilmelerinin temel şartı birden fazla, ihtilaflı ve karmaşık amaçları mevcut kısıtlara göre değerlendirip en doğru kararı verebilmektir. Birçok matematiksel programlama problemi, karar verici tarafından kısıtlara bağlı olarak amaç fonksiyonlarının bir araya getirilmesinden oluşmaktadır. Bu çalışmada Minmaks tabanlı yaklaşımla optimal sistemin tasarımının nasıl yapılacağı araştırılmıştır. Araştırmada Minmaks Hedef Programlama ile MA yaklaşımı olarak da bilinen bir Bulanık Hedef yaklaşımı kullanılmıştır. El sanatları üretimi yapan bir işletmede kaynak miktarlarının optimal seviyede belirlenebilmesi için Çok Amaçlı De novo programlama olarak kurulan problemin çözümü bu iki yaklaşıma göre yapılmıştır. MA yaklaşımına göre problemin çözülebilmesi için bütçe kısıtı bir hedef olarak düzenlenmiş ve bir çözüm önerisi yapılmıştır. Elde edilen sonuçlara göre Minmaks Programming ve MA yaklaşımının çözüm sonuçlarının aynı olduğu belirlenmiştir.

Anahtar Kelimeler

• De Novo Programlama,Bulanık Hedef Programlama,Minmaks Hedef Programlama,Optimal Sistem Tasarımı

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