Computational complexity of stochastic programming problems

Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast amount of literature on the subject has appeared. The researchers in the field have never ceased to emphasize the inherent difficulties in solving stochastic programming problems, without ever giving a theoretical justification of this common feeling. Recent developments in the theory of computational complexity allow us to establish the theoretical complexity of most stochastic programming models studied in the literature. Our results confirm the general feelings alluded to above.