Decisions often need to be made in situations where one has incomplete knowledge about some of the parameters of the problem that he is addressing. This is for example the case in a problem of portfolio selection where the future value of an asset is uncertain or in an inventory management problem (e.g., airline fleet composition) where the future market demand for a product might be subject to changing. Distributionally robust optimization is a generalization of stochastic programming that can provide essential guidance in managing such decision problems since it can account for ambiguity in the choice of a distribution model. Such ambiguity is often present in practice thus a solution that is based purely on stochastic programming can be misleading.
In this talk, I will present computational, theoretical and empirical evidence that justifies choosing the robust decisions when such ambiguity is present. I will also propose tractable methods for bounding the gains that might otherwise be achieved if the ambiguity was resolved prior to taking the decision. Finally, I will discuss issues that remain to be resolved in order to help distributionally robust optimization and its derivatives become common practice.