Doğrusal Tamsayılı Programlama Problemlerinin Çözümü İçin Yeni Alternatif Bir Algoritma

Year 2021, , 93 - 98, 01.12.2021

Kadriye Şimşek Alan

https://doi.org/10.31590/ejosat.1019251

Abstract

Bu çalışmada doğrusal bir amaç fonksiyonuna ve doğrusal eşitlik veya eşitsizliklereden oluşan kısıtlara sahip olan Doğrusal Tamsayılı Programlama (DTP) Problemlerinin çözümü için yeni alternatif bir yöntem ve yeni alternatif bir algoritma sunulmaktadır. Yöntemimiz basit cebirsel işlemler ve matematik programlamaya dayanmaktadır. Doğrusal Tamsayılı Programlama Problemlerinin çözümünde kullanılan pek çok yöntem olmasına rağmen, bu yöntemlerin birçoğu uygulamada ve hesaplamada bazı güçlüklere sahiptir. Bu güçlüklere sahip olmayan yöntemimiz, diğer yöntemlere göre problemin sahip olduğu değişken sayısına daha az hassasdır. Bundan dolayı da çok sayıda değişkene sahip olan gerçek yaşam problemlerinin çözümünde de kullanılabilir. Ayrıca verilen problemin tüm alternatif çözümlerini de karar vericiye sunar. Önerilen yöntemin nasıl uygulandığını gösteren bir sayısal örnek verilerek Maple programlama dilinde kodlaması yapılmışıtır.

Keywords

Doğrusal tamsayılı programlama, Doğrusal Diophantine denklemi, Optimum değer, Optimum çözüm, Optimal hiperdüzlem.

Supporting Institution

Yıldız Teknik Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Project Number

FBA-2021-4032

Thanks

Bu çalışmaya olan desteklerinden dolayı Yıldız Teknik Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimine teşekkür ederim.

A Novel Alternative Algorithm for Solving Linear Integer Programming Problems

Abstract

In this study, a novel alternative method and a novel alternative algorithm are presented for the solution of Linear Integer Programming Problems that have a linear objective function and constraints consisting of linear equations or inequalities. Our method is based on simple algebraic operations and mathematical programming. Although there are many methods used in solving Linear Integer Programming Problems, most of these methods have some difficulties in application and computation. Our method, which does not have these difficulties, is easy to implement and less sensitive to the number of variables fo the problem than other methods. Therefore, it can also be used in solving real-life problems that have a large number of variables. It also presents all alternative solutions to the given problem to the decision maker. A numerical example showing how the proposed method is applied is given and coded in the Maple programming language.

Keywords

Integer linear programming, Linear Diophantine equations, Integer programming problems, Optimal solution.

Project Number

FBA-2021-4032

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