Modification Interior-Point Method for Solving Interval Linear Programming

Abstract

Linear programming is mathematical programming developed to deal with optimization problems involving linear equations in the objective and constraint functions. One of the basic assumptions in linear programming problems is the certainty assumption. Assumption of certainty shows that all coefficients variable or decision variables in the model are constants that are known with certainty. However, in real situations or problems, there may be uncertain coefficients or decision variables. Based on the concept and theory of interval analysis, this uncertainty problem is anticipated by making approximate values in intervals to develop linear interval programming. The development of interval linear programming starts from linear programming with interval-shaped coefficients, both in the coefficient of the objective function and the coefficient of the constraint function. It was subsequently developed into linear programming with coefficients and decision variables in intervals, commonly known as interval linear programming. Until now, the completion of interval linear programming is based on the calculation of the interval limit. The initial procedure for the solution is to change the linear programming model with interval variables into two classical linear programming models. Finally, the optimal solution in the form of intervals is obtained by constructing two models. This paper provides an alternative solution to directly solve the linear interval programming problem without building it into two models. The solution is done using the interval arithmetic approach, while the method used is the modified interior-point method.