On the two‐stage problem of linear stochastic programming with quantile criterion and discrete distribution of the random parameters

Consideration was given to the two‐stage problem of stochastic linear programming with a discrete distribution of the random parameter vector. The property of continuity of the quantile function in strategy was proved, the sufficient conditions for existence of solution were formulated, and an algorithm to determine the guaranteeing solution was constructed on the basis of the confidence method and the duality theorem. A deterministic equivalent of the considered problem in the form of a linear programming problem was given for the scalar case.