Avoid maximum cost method for determining the initial basic feasible solution of the transportation problem

Year 2022, Volume: 28 Issue: 4, 569 - 576, 31.08.2022

Özcan Mutlu Kenan Karagül Yusuf Şahin

Abstract

The transportation problem is an optimization problem related to determining the transportation plan that will ensure the transportation of products from supply points to demand points with minimum total cost. Although this problem can be modeled as a linear programming model because of its special structure, it is usually solved in two phases: finding the initial basic solution and finding the optimal solution. Thus, finding a good initial solution is important, especially in large problems since it will reduce the number of steps required in the second phase. To date, many approaches have been developed to find the initial basic solution. In this study, a new method called avoid maximum cost method is proposed for determining the initial basic solution of the transportation problem. The advantage of this algorithm is that it is easy to understand and implement. The avoid maximum cost method is applied to test problems and compared with six well-known initial solution methods. The results show that the proposed method produces a consistent and very good initial basic feasible solution. In addition, because of its simplicity, this method can be used as an alternative method for an initial basic feasible solution besides well-known methods in teaching.

Keywords

Transportation, Initial solution, Approximation method

Ulaştırma probleminin başlangıç uygun çözümünün belirlenmesi için en büyük maliyetten kaçınma yöntemi

Abstract

Ulaştırma Problemi, ürünlerin arz noktalarından talep noktalarına minimum toplam maliyetle taşınmasını sağlayacak taşıma planının belirlenmesi ile ilgili bir optimizasyon problemidir. Bu problem, özel yapısı nedeniyle bir doğrusal programlama modeli olarak modellenebilse de genellikle başlangıç temel çözümünü bulma ve en uygun çözümü bulma olmak üzere iki aşamada çözülür. Bu nedenle, özellikle büyük problemlerde, ikinci aşamada gereken adım sayısını azaltacağından, iyi bir başlangıç çözümü bulmak önemlidir. Bugüne kadar başlangıç temel çözümünü bulmak için birçok yaklaşım geliştirilmiştir. Bu çalışmada, ulaştırma probleminin başlangıç çözümünün belirlenmesi için maksimum maliyetten kaçınma yöntemi adı verilen yeni bir yöntem önerilmiştir. Bu algoritmanın avantajı, anlaşılması ve uygulanmasının kolay olmasıdır. Maksimum maliyetten kaçınma yöntemi test problemlerine uygulanmış ve iyi bilen altı başlangıç çözüm yöntemi ile karşılaştırılmıştır. Sonuçlar önerilen yöntemin tutarlı ve iyi başlangıç uygun çözümler ürettiğini göstermektedir. Ayrıca, çok basit olması nedeniyle bu yöntem öğretimde çok bilinen yöntemlerle birlikte başlangıç uygun çözümlerin bulunmasında alternatif olarak kullanılabilir

Keywords

Ulaştırma, Başlangıç çözüm, Yaklaşım yöntemi

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