SOLUTION OF A MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM HAVING ROUGH INTERVAL COEFFICIENTS USING ZERO-SUM GAME

Öz

In this paper, a set of compromise solutions is found for the multi-objective linear programming with rough interval coefficients (MOLPRIC) problem by proposing a two-phased algorithm. In the first phase, the MOLPRIC problem is separated into single-objective LPRIC problems considering the number of objective functions, and the rough optimal solution of each LPRIC problem is found. In the second phase, a zero-sum game is applied to find the rough optimal solution. Generally, the weighted sum method is used for determining the trade-off weights between the objective functions. However, it is quite inapplicable when the number of objective functions increases. Thus, the proposed algorithm has an advantage such that it provides an easy implementation for the MOLPRIC problems having more than two objective functions. With this motivation, applying a zero-sum game among the distinct objective values yields different compromise solutions.

Anahtar Kelimeler

• Compromise solution
• Game theory
• Multi-objective linear programming problem
• Rough interval coefficient

KABA ARALIKLI KATSAYILARA SAHIP ÇOK AMAÇLI DOĞRUSAL PROGRAMLAMA PROBLEMİNİN SIFIR TOPLAMLI OYUN İLE ÇÖZÜMÜ

Öz

Kaba sayılardan oluşan aralıklara sahip katsayılar içeren, çok amaçlı doğrusal programlama (MOLPRIC) problemi için bir çözüm önerisinde bulunulmuştur. Bu çalışmada ele alınan probleme uzlaşmacı çözümler kümesi önerilmiş olup çözüm algoritması iki aşamalı olarak düzenlenmiştir. İlk aşamada, MOLPRIC probleminin barındırdığı amaç fonksiyonlarının sayısı dikkate alınarak her bir tek amaçlı LPRIC kaba optimal çözümü bulunmuştur. İkinci aşamada ise MOLPRIC probleminin kaba optimal çözümünü bulmak üzere sıfır toplamlı oyundan yararlanılmıştır. Çok amaçlı problemlerin çözüm sürecinde amaç fonksiyonları arasındaki ödünleşim ağırlıklarının belirlenmesinde genellikle ağırlıklı toplam yöntemi kullanılmaktadır. Ancak amaç fonksiyonlarının sayısı arttığında bu geleneksel yöntem uygulamada zorluk çıkarabilmektedir. Dolayısıyla önerilen algoritmanın özgünlüğü, ikiden fazla amaç fonksiyonuna sahip MOLPRIC problemlerine kolay uygulanabilir olmasıdır. Bu motivasyonla, farklı amaç değerleri arasında sıfır toplamlı oyunun uygulanması, farklı uzlaşık çözümlerin bulunmasını sağlamaktadır.

Anahtar Kelimeler

• Çok amaçlı doğrusal programlama problemi
• Kaba sayılı aralık
• Oyun teorisi
• Uzlaşık çözüm

Kaynakça

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