A new algorithm to obtain the optimal solution set of the interval linear programming

To describe parameters of the real world systems the interval linear programming (ILP) is an efficient device. In this paper, we introduce a new algorithm, where, firstly an arbitrary characteristic model of the ILP model is chosen and solved, and the index set of its active constraints is obtained. Then, by attention to the index set of the active constraints a system of interval linear equations is formed and solved by using the enclosure method. If all components of the interval solutions of this system are strictly nonnegative, then the optimal solution set of the ILP model is determined as the intersection of the zone generated by the best model constraints and the worst model active constraints with inverse sign. Finally, a comparison between the solutions obtained through the above-mentioned algorithm and Monte Carlo simulation method is conducted to demonstrate the robustness of the above-mentioned algorithm.

Keywords:

Optimal solution set , Interval linear programming , System of interval linear equations , Monte Carlo simulation