Scenario Optimization for Multi-Stage Stochastic Programming Problems

The field of multi-stage stochastic programming provides a rich modelling framework to tackle a broad range of real-world decision problems. In order to numerically solve such programs once they get reasonably large the infinite-dimensional optimization problem has to be discretized. The stochastic optimization program generally consists of an optimization model and a stochastic model. In the multi-stage case the stochastic model is most commonly represented as a multi-variate stochastic process. The most common technique to calculate an useable discretization is to generate a scenario tree from the underlying stochastic process. Scenario tree generation is examplified by reviewing one specific algorithm based on multi-dimensional facility location applying backward stagewise clustering.