<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this study, a novel alternative method based on parameterization for solving Integer Linear Programming (ILP) problems having three variables is developed. This method, which is better than the cutting plane and branch boundary method, can be applied to pure integer linear programming problems with m linear inequality constraints, a linear objective function with three variables. Both easy to understand and to apply, the method provides an effective tool for solving three variable integer linear programming problems. The method proposed here is not only easy to understand and apply, it is also highly reliable, and there are no computational difficulties faced by other methods used to solve the three-variable pure integer linear programming problem. Numerical examples are provided to demonstrate the ease, effectiveness and reliability of the proposed algorithm.</p></abstract>

In this study, a novel alternative method based on parameterization for solving Integer Linear Programming (ILP) problems having three variables is developed. This method, which is better than the cutting plane and branch boundary method, can be applied to pure integer linear programming problems with m linear inequality constraints, a linear objective function with three variables. Both easy to understand and to apply, the method provides an effective tool for solving three variable integer linear programming problems. The method proposed here is not only easy to understand and apply, it is also highly reliable, and there are no computational difficulties faced by other methods used to solve the three-variable pure integer linear programming problem. Numerical examples are provided to demonstrate the ease, effectiveness and reliability of the proposed algorithm.

A Novel Alternative Algorithm for Solving Integer Linear Programming Problems Having Three Variables

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this study, a novel alternative method based on parameterization for solving Integer Linear Programming (ILP) problems having three variables is developed....

A Novel Alternative Algorithm for Solving Integer Linear Programming Problems Having Three Variables

Published Online: Dec 10, 2020

Page range: 27 - 35

Received: Apr 21, 2020

Accepted: Sep 08, 2020

DOI: https://doi.org/10.2478/cait-2020-0045

Keywords
Linear Integer Programming (LIP), linear Diophantine equations, optimal hyperplane, pure integer programming problems, optimal solution

© 2020 Kadriye Simsek Alan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Novel Alternative Algorithm for Solving Integer Linear Programming Problems Having Three Variables

Published Online: Dec 10, 2020

Page range: 27 - 35

Received: Apr 21, 2020

Accepted: Sep 08, 2020

DOI: https://doi.org/10.2478/cait-2020-0045

KeywordsLinear Integer Programming (LIP), linear Diophantine equations, optimal hyperplane, pure integer programming problems, optimal solution

© 2020 Kadriye Simsek Alan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Linear Integer Programming (LIP), linear Diophantine equations, optimal hyperplane, pure integer programming problems, optimal solution