Robust solutions in stochastic linear programming

The recent developments in stochastic linear programming are reviewed here broadly in their applied aspects. They include non-parametric methods which are applicable in situations of incomplete knowledge and partial uncertainty. This framework is shown to be most suitable for developing robust optimal solutions. For instance, a class of non-parametric methods based on the minimax principle and the criteria of stochastic dominance is developed here to illustrate its wide scope of application. It is shown that this class of methods provides a measure of robustness through the adoption of a cautious policy. Some examples are discussed using the recent field of data envelopment analysis.