A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice

While methods for optimization under uncertainty have been studied intensely over the past decades, the explicit consideration of the interplay between uncertainty and time has gained increasing attention rather recently. Problems requiring a sequence of decisions in reaction to uncertainty realizations are of crucial relevance in real-world applications, e.g., supply chain planning, scheduling, or finance. Several methods emphasizing varying aspects of these problems have been developed, mainly triggered by a particular application. Although these methods all intend to solve a similar underlying problem, they differ strongly with respect to the uncertainty representation, the prescriptive solution information they provide and the means of performance evaluation. The result is a fragmented picture of uncertain multi-stage problems – both from a methodological and an application-oriented perspective. It fails to interconnect results from different disciplines or even comparing strengths and weaknesses of individual methods in particular applications. This review aims at integrating the different methods for solving uncertainty inflicted multi-stage optimization problems into a broader picture, thereby paving the way for more comprehensive approaches to sequential decision making under uncertainty. For this purpose, a description of the methods along with their historic development is given first. Secondly, an overview on their main areas of application is provided. We conclude that decoupling uncertainty models from solution methods and developing standardized performance measures represent key steps for organizing multi-stage optimization under uncertainty and for eliciting further potentials of yet unexplored combinations of uncertainty models and solution methods.