Dört Değişkenli Doğrusal Tamsayılı Programlama Problemlerinin Çözümü İçin Yeni Bir Alternatif Algoritma

Year 2021, Issue: 29, 81 - 86, 01.12.2021

Kadriye Şimşek Alan

https://doi.org/10.31590/ejosat.1020212

Abstract

Bu çalışmada, dört değişkenli Tamsayılı Doğrusal Programlama problemlerinin çözümü için parametrizasyona dayanan yeni iterativ bir yöntem önerilmiş ve bir algoritma sunulmuştur. Dört değişkenli DTP problemlerinin çözümünde kesme düzlemi yöntemi ve dal-sınır yöntemlerinden daha iyi olan yöntemimiz, kısıtlama sayısından bağımsız olarak kolaylıkla uygulanabilmektedir. Ayrıca yöntemimizde tüm alternatif çözümler bulunur ve karar vericiye sunulur. Önerilen yöntem uygulanarak sayısal bir örnek çözülmüştür.

Keywords

Tamsayılı doğrusal programlama, Doğrusal Diophantine denklemleri, Tamsayılı programlama problemleri, Optimal çözüm.

Supporting Institution

Yildiz Technical University Scientific Research Projects Coordination Unit

Project Number

FBA-2021-4032.

Thanks

Bu çalışmaya olan destekleri içinYıldız Teknik Üniversitesi Proje Koordinasyon birimine teşekkür ederim.

A Novel Alternative Algorithm for Solving Linear Integer Programming Problems with Four Variables

Abstract

In this paper, new iterative method is proposed based on parametrization for solving Integer Linear Programming (ILP) problems with four variables and an algorithm is provided. Our method, which is better than the cutting plane method and branch and bound methods in solving ILP problems with four variables, can be easily applied regardless of the number of constraints. In addition, in our method, all alternative solutions are found and presented to the decision maker. A numerical example is solved by applying the proposed method.

Keywords

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

Project Number

FBA-2021-4032.

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