A Comparative Analysis of Various Optimization Methods for Solving Fully Fuzzy Transportation Problems

Leyla İşbilen Yücel

Article Details

A Comparative Analysis of Various Optimization Methods for Solving Fully Fuzzy Transportation Problems

Authors:

Leyla İşbilen Yücel

Publisher:

Pamukkale University

Main Topics:

Yöneylem Araştırması

Journal:

Pamukkale Üniversitesi İşletme Araştırmaları Dergisi Vol.11 Issue 2, pp.572-591

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001332296

pISSN:

2757-7260

Keywords:

Abstract:

 This study investigates the solution of a Trapezoidal Fuzzy Transportation Problem FTP using Basirzadehs Fuzzy Ranking Approach through various optimization methods. The FTP was drawn from Pandian and Natarajans 2010 article in Applied Mathematical Sciences. They used the Fuzzy Zero Point Method to solve the FTP. However, the fact that this method has eleven steps, each requiring fuzzy operations, makes it a compelling process. To point out this complexity and to illustrate how easy to get the result, Basirzadehs method has been adopted in this study. In this method, the fuzzy data is converted into crip data, and a transportation matrix is created. Then it can be solved by any transportation method and the results may remain crisp or they might be fuzzified. In this study, firstly, the FTP has been solved using the Fuzzy Zero Point Method. Not only the initial cost table and final allocation table have been shared with readers, but also all intermediate steps of the fully fuzzy solution have been demonstrated. Subsequently, some common optimization methods used in transportation problems such as Northwest Corner, Least Cost, Russel, and Vogels methods, have been applied to Basirzadehs method and the results have been compared. Russels Method seems to be the best among these methods because it yielded the lowest transportation cost.

 This study investigates the solution of a Trapezoidal Fuzzy Transportation Problem FTP using Basirzadehs Fuzzy Ranking Approach through various optimization methods. The FTP was drawn from Pandian and Natarajans 2010 article in Applied Mathematical Sciences. They used the Fuzzy Zero Point Method to solve the FTP. However, the fact that this method has eleven steps, each requiring fuzzy operations, makes it a compelling process. To point out this complexity and to illustrate how easy to get the result, Basirzadehs method has been adopted in this study. In this method, the fuzzy data is converted into crip data, and a transportation matrix is created. Then it can be solved by any transportation method and the results may remain crisp or they might be fuzzified. In this study, firstly, the FTP has been solved using the Fuzzy Zero Point Method. Not only the initial cost table and final allocation table have been shared with readers, but also all intermediate steps of the fully fuzzy solution have been demonstrated. Subsequently, some common optimization methods used in transportation problems such as Northwest Corner, Least Cost, Russel, and Vogels methods, have been applied to Basirzadehs method and the results have been compared. Russels Method seems to be the best among these methods because it yielded the lowest transportation cost.

 This study investigates the solution of a Trapezoidal Fuzzy Transportation Problem FTP using Basirzadehs Fuzzy Ranking Approach through various optimization methods. The FTP was drawn from Pandian and Natarajans 2010 article in Applied Mathematical Sciences. They used the Fuzzy Zero Point Method to solve the FTP. However, the fact that this method has eleven steps, each requiring fuzzy operations, makes it a compelling process. To point out this complexity and to illustrate how easy to get the result, Basirzadehs method has been adopted in this study. In this method, the fuzzy data is converted into crip data, and a transportation matrix is created. Then it can be solved by any transportation method and the results may remain crisp or they might be fuzzified. In this study, firstly, the FTP has been solved using the Fuzzy Zero Point Method. Not only the initial cost table and final allocation table have been shared with readers, but also all intermediate steps of the fully fuzzy solution have been demonstrated. Subsequently, some common optimization methods used in transportation problems such as Northwest Corner, Least Cost, Russel, and Vogels methods, have been applied to Basirzadehs method and the results have been compared. Russels Method seems to be the best among these methods because it yielded the lowest transportation cost.

 Bu çalışma tümüyle yamuk bulanık sayılardan oluşan bir ulaştırma probleminin Basirzadehin bulanık sayıların sıralanmasına dayanan yöntemi benimsenerek, çeşitli optimizasyon yöntemleri ile çözülmesini konu almaktadır. Çözümlemelerin yapıldığı sayısal örnek, Pandian ve Natajaranın 2010da Applied Mathematical Sicences dergsindeki makalelerinden alınmıştır. Pandian ve Natajaran, bulanık ulaştırma probleminin çözümünde bulanık sıfır noktası yöntemini kullanmışlardır. Fakat onbir adımdan oluşan ve her adımında bulanık sayılarla işlemler yapmayı gerektiren bu yöntemin uygulanması zorlu bir süreçtir. Bu zorluğu gözler önüne sermek ve sonucu elde etmenin ne kadar kolay olduğunu göstermek için, bu çalışmada Basirzadehin yöntemi benimsenmiştir. Bu yöntemde, bulanık veri keskin veriye dönüştürülmekte ve bir taşıma matrisi oluşturulmaktadır. Daha sonra herhangi bir optimizasyon yöntemi ile çözülebilmekte ve sonuçlar keskin kalabilmekte ya da bulandırılabilmektedir. Bu çalışmada, ilk olarak FTP, Bulanık Sıfır Noktası Yöntemi kullanılarak çözülmüştür. Sadece başlangıç maliyet tablosu ve son atama tablosu okuyucularla paylaşılmamış, aynı zamanda tam bulanık çözümün tüm ara adımları da gösterilmiştir. Ardından, aynı bulanık ulaştırma problemi bulanık sıralama yaklaşımı benimsenerek, Kuzey Batı Köşesi, En Düşük Maliyet, Russel ve Vogelin optimizasyon yöntemleri ile çözülmüş ve sonuçları kıyaslanmıştır. Bu yöntemler arasında en iyi yöntemin, en düşük ulaşım maliyetini sağlayan Russel Metodu olduğu söylenebilir.

Article Details

A Comparative Analysis of Various Optimization Methods for Solving Fully Fuzzy Transportation Problems

Authors:

Leyla İşbilen Yücel

Publisher:

Pamukkale University

Main Topics:

Yöneylem Araştırması

Journal:

Pamukkale Üniversitesi İşletme Araştırmaları Dergisi Vol.11 Issue 2, pp.572-591

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001332296

pISSN:

2757-7260

Fuzzy transportation problem

ranking of fuzzy numbers

fuzzy zero-point method

northwest corner method

least cost method

Russel’s methodBulanık ulaştırma problemi

bulanık sayıların sıralanması

bulanık sıfır noktası yöntemi

kuzey batı köşe yöntemi

en düşük maliyet yöntemi

Russel yöntemi

Vogel yöntemi.

Issues

Article Details

Authors: Leyla İşbilen Yücel

Publisher: Pamukkale University

Main Topics: Yöneylem Araştırması

Journal: Pamukkale Üniversitesi İşletme Araştırmaları Dergisi Vol.11 Issue 2, pp.572-591

Document Type: Article

Publication Date: 12/2024

Document Language: English

Document ID (Org No.): 2001332296

pISSN: 2757-7260

Issues

Authors:

Leyla İşbilen Yücel

Publisher:

Pamukkale University

Main Topics:

Yöneylem Araştırması

Journal:

Pamukkale Üniversitesi İşletme Araştırmaları Dergisi Vol.11 Issue 2, pp.572-591

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001332296

pISSN:

2757-7260