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Mathematical Problems in Engineering
Volume 2011, Article ID 840137, 13 pages
Research Article

A Numerical Method for Two-Stage Stochastic Programs under Uncertainty

Facultad de Ingeniería, Universidad Diego Portales, Avenue Ejército 441, Santiago 8370191, Chile

Received 12 January 2011; Revised 18 April 2011; Accepted 6 May 2011

Academic Editor: Angelo Luongo

Copyright © 2011 Paul Bosch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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?