Scenario Reduction Techniques in Stochastic Programming

Stochastic programming problems appear as mathematical models for optimization problems under stochastic uncertainty. Most computational approaches for solving such models are based on approximating the underlying probability distribution by a probability measure with finite support. Since the computational complexity for solving stochastic programs gets worse when increasing the number of atoms (or scenarios), it is sometimes necessary to reduce their number. Techniques for scenario reduction often require fast heuristics for solving combinatorial subproblems. Available techniques are reviewed and open problems are discussed.