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

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.