Data-driven multi-stage scenario tree generation via statistical property and distribution matching

The objective of this paper is to bring systematic methods for scenario tree generation to the attention of the Process Systems Engineering community. In this paper, we focus on a general, data-driven optimization-based method for generating scenario trees, which does not require strict assumptions on the probability distributions of the uncertain parameters. This method is based on the Moment Matching Problem (MMP), originally proposed by Høyland & Wallace (2001). In addition to matching moments, and in order to cope with potentially under-specified MMP, we propose matching (Empirical) Cumulative Distribution Function information of the uncertain parameters. The new method gives rise to a Distribution Matching Problem (DMP) that is aided by predictive analytics. We present two approaches for generating multi-stage scenario trees by considering time series modeling and forecasting. The aforementioned techniques are illustrated with a motivating production planning problem with uncertainty in production yield and correlated product demands.