Algorithm to optimize the quantile criterion for the polyhedral loss function and discrete distribution of random parameters

For the vector of random parameters with discrete distribution and finite number of realizations, consideration was given to the problem of stochastic linear programming with a quantile criterion. The sufficient conditions for existence of problem solution were formulated. A method of reduction of the original problem to the mixed linear programming problem of high dimension was proposed. For the resulting problem, a solution algorithm was constructed on the basis of the methods of decomposition of the linear programming problems.