A Numerical Method for Two-Stage Stochastic Programs under Uncertainty

Motivated by problems coming from planning and operational management in power generation companies, this work extends the traditional two-stage linear stochastic program by adding probabilistic constraints in the second stage. In this work we describe, under special assumptions, how the two-stage stochastic programs with mixed probabilities can be treated computationally. We obtain a convex conservative approximations of the chance constraints defined in second stage of our model and use Monte Carlo simulation techniques for approximating the expectation function in the first stage by the average. This approach raises with another question: how to solve the linear program with the convex conservative approximation (nonlinear constrains) for each scenario?