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An Alternative Algorithm for Solving Pure Integer Linear Programming Problems Having Two Variables

Kadriye Simsek Alan, Inci Albayrak, Mustafa Sivri, Coskun Guler in Algorithms

International Journal of Applied Information Systems
Year of Publication: 2019
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors:Kadriye Simsek Alan, Inci Albayrak, Mustafa Sivri, Coskun Guler
10.5120/ijais2019451826
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  1. Kadriye Simsek Alan, Inci Albayrak, Mustafa Sivri and Coskun Guler. An Alternative Algorithm for Solving Pure Integer Linear Programming Problems Having Two Variables. International Journal of Applied Information Systems 12(25):6-9, November 2019. URL, DOI BibTeX

    @article{10.5120/ijais2019451826,
    	author = "Kadriye Simsek Alan and Inci Albayrak and Mustafa Sivri and Coskun Guler",
    	title = "An Alternative Algorithm for Solving Pure Integer Linear Programming Problems Having Two Variables",
    	journal = "International Journal of Applied Information Systems",
    	issue_date = "November, 2019",
    	volume = 12,
    	number = 25,
    	month = "November",
    	year = 2019,
    	issn = "2249-0868",
    	pages = "6-9",
    	url = "http://www.ijais.org/archives/volume12/number25/1069-2019451826",
    	doi = "10.5120/ijais2019451826",
    	publisher = "Foundation of Computer Science (FCS), NY, USA",
    	address = "New York, USA"
    }
    

Abstract

An alternative algorithm is proposed, based on parametrization for solving a special class of integer linear programming (ILP) problems when the objective function is linear and the constraints are in the form of linear inequality. Although there are popular methods in the literature having widespread impact they are known to have some difficulties in terms of computation. To overcome these difficulties, a parameter-based algorithm that could be applied reliably and easily to (ILP) problems with two variables and no restriction on the constraints is proposed. The flow of the algorithm provides a set constructed by variable values that depend on the parameter. Thus, the solution satisfying the constraints can be selected easily from this set. The proposed algorithm is remarkable in that it can be applied easily even when the number of restrictions increases.

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Keywords

Linear integer programming, Linear Diophantine equations, optimal hyperplane