Initial Basic Feasible Solution Approach for Transportation Problem: Logarithmic Fermi Approximation

Year 2025, Volume: 10 Issue: 28, 695 - 711

Kenan Karagül

https://doi.org/10.25204/iktisad.1578630

Abstract

Transportation problems are considered as a fundamental topic in operations research. In large-scale and complex network structures, initial solutions provide cost effectiveness by influencing the quality and speed of algorithms. Transportation problems aim to balance supply-demand and minimize costs. Appropriate initial solutions save time by producing results close to the optimal solution. Using a single appropriate initial solution algorithm for balanced and unbalanced transportation problems can be more efficient. The new approach proposed in this study is called the Logarithmic Fermi Approach. To analyze the performance of the approach, P1 and P2 test problems with different cost ranges were generated. Analyses have shown that Logarithmic Fermi Method (LFM) and Karagül-Şahin Approximation Method (KSAM) stand out in balanced and unbalanced problems, while North-West Corner Method (NCW) demonstrates poor performance. In large-scale problems, Logarithmic Fermi Method (LFM) and Least Cost Method (LCM) algorithms have produced results close to the optimal solution. The proposed method has shown to have a competitive structure in the analyses.

Keywords

Transportation Problem , Basic Initial Feasible Solution , KSAM , LCM

Ulaştırma Problemi İçin Uygun Başlangıç Çözüm Yaklaşımı: Logaritmik Fermi Yaklaşımı

Abstract

Yöneylem araştırmasında ulaştırma problemleri temel bir konu olarak ele alınır. Büyük ölçekli ve karmaşık ağ yapılarında, başlangıç çözümleri algoritmaların kalitesini ve hızını etkileyerek maliyet etkinliği sağlar. Ulaştırma problemlerinde arz-talep dengesi ve maliyetlerin minimize edilmesi amaçlanır. Uygun başlangıç çözümleri optimal çözüme yakın sonuçlar üreterek zaman tasarrufu sağlar. Dengeli ve dengesiz ulaştırma problemleri için tek bir uygun başlangıç çözüm algoritması kullanmak daha verimli olabilir. Bu çalışmada önerilen yeni yaklaşıma Logaritmik Fermi Yaklaşımı adı verilmiştir. Yaklaşımın performansını analiz etmek için farklı maliyet aralıklarına sahip P1 ve P2 test problemleri üretilmiştir. Analizler, dengeli ve dengesiz problemlerde Logaritmik Fermi Yaklaşımı (LFM) ve Karagül-Şahin Yaklaşım Metodu (KSAM)'ın öne çıktığını, Kuzey-Batı Köşe Yöntemi (NCW)'nin ise düşük performans gösterdiğini ortaya koymuştur. Büyük ölçekli problemlerde Logaritmik Fermi Yaklaşımı (LFM) ve En Küçük Maliyetli Göze Metodu (LCM) algoritmaları, optimal çözüme yakın sonuçlar üretmiştir. Önerilen yöntemin analizlerde rekabetçi bir yapısının olduğu görülmüştür.

Keywords

Ulaştırma Problemi , Uygun Başlangıç Çözüm , KSAM , En Küçük Maliyetli Göze , Kuzey-Batı Köşe

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