PERTURBATION METHOD FOR SOLVING OF LINEAR PROGRAMMING PROBLEMS WITH A PARAMETER
The method earlier proposed by authors of successive elimination of variables in the system of linear inequalities that correspond to the problem of linear programming allows one to find the exact analytical solution of problems with variable coefficients depending on the parameter also. However, in case of alternate signs of the variables thorough examination of each parameter interval where the coefficients retain their sine is required. An effective method for finding an approximate analytical solution of linear programming problem with variable coefficients in the case of weak relative change of the coefficients is proposed in this paper. It is based on widely used in applied mathematics perturbation method, in other words the method of a small parameter, allowing building a simple iteration scheme. The accuracy of solution of about 1 % is reached in a few iterations. The presented procedure can be easily generalized to a multi-parameter problem.