Abstract. We consider a two-stage stochastic programming model with quantile criterion, as well as models with a probabilistic constraint on the random value of the objective function of the second stage. These models allow us to formalize the requirements for the reliability and safety of the system being optimized and to optimize the system performance under extreme conditions. We propose a method of equivalent transformation of these models under discrete distribution of random parameters to mixed-integer programming problems. The number of additional integer (Boolean) variables in these problems equals to the number of possible values of the vector of random parameters. The obtained mixed optimization problems can be solved by powerful standard discrete optimization software. To illustrate the approach, the results of numerical experiment for the problem of small dimension are presented. Refs: 35 titles.

Keywords: stochastic programming, two-stage problems, quantile programming, probabilistic constraints, deterministic equivalent, mixed-integer optimization problems, discrete programming.