A Solution of Linear Programming With Interval Variables Using the Interior Point Method Based on Interval Boundary Calculations

Abstract

Linear programming with interval variables is the development of linear programming with interval coefficients. In this paper, linear programming with interval variables is solved using the interior point method based on interval boundary calculations. The solution’s initial procedure is to change the linear programming model with interval variables into a pair of classical linear programming models. This pair of two classical linear programming models corresponds to an interval boundary called the least upper bound and the greatest lower bound. The least upper bound is determined using the largest feasible region and the greatest lower bound is determined by using the smallest feasible region. The least upper bound and the greatest lower bound are obtained using the interior point method. Finally, the optimal solution in the form of intervals is obtained by constructing the two models. This paper provides an alternative solution to solve the linear interval programming problem by using the interior point method.