Robust Optimization with practical application

Abstract

The purpose of this paper is applying the robustness in Linear programming(LP) to get rid of uncertainty problem in constraint parameters, and find the robust optimal solution, to maximize the profits of the general productive company of vegetable oils for the year 2019, through the modify on a mathematical model of linear programming when some parameters of the model have uncertain values, and being processed it using robust counterpart of linear programming to get robust results from the random changes that happen in uncertain values ​​of the problem, assuming these values belong to the uncertainty set and selecting the values that cause the worst results and to depend build a robust linear model on it, and then comparing between robust optimal results with usual optimal results.

      In this paper has been reached to the most important results, it is possible that a simple neglecting of uncertainty in the parameters' values causes a decrease in profits, so in case increase the percentage of impurities in raw materials to the maximum of their expected cases, caused a decrease in the concentration of active substance needed to produce planned amount, that make decreases production and therefore reducing of revenue the value of (67,883,826.8281) IQD per year from the expected profit, as that total of expected profit is (537,921,100) IQD, and when this value decreases because the values change randomly, the profits are (470,037,273.172) IQD in the worst expected cases. While when the robust model was applied, the total profit was (476,269,200) IQD. In contrast ensures that this value is not decreased at any random change to the value was happening, because the robust model was built in its worst-case expected. Also, it is possible to guarantee that any violation of the constraint was avoided in the event of random variations that obtain in uncertainty parameter value when applying a robust style.