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

• Published in: Computers & chemical engineering Vol. 68; pp. 7 - 23
• Main Authors: Calfa, B.A., Agarwal, A., Grossmann, I.E., Wassick, J.M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 04.09.2014; Elsevier
• Subjects: Analytics; Applied sciences; Chemical engineering; Communities; Computer science; control theory; systems; Computer simulation; Control theory. Systems; Data processing. List processing. Character string processing; Distribution Matching Problem; Exact sciences and technology; Matching; Mathematical models; Memory organisation. Data processing; Process control. Computer integrated manufacturing; Process Systems Engineering; Production planning; Scenario generation; Software; Stochastic Programming; Time series; Time series forecasting; Trees; Stochastic Programming; Distribution Matching Problem; Time series forecasting; 90C90; 90C15; Scenario generation; Process Systems Engineering; Analytics; Information integration; Process engineering; Statistical distribution; Probability distribution; Data driven modelling; Optimization; Uncertain system; Production planning; Marginal distribution; Distribution function; Tree; Script; Statistical analysis; Empirical method; Time series; Multistage apparatus; Forecasting; Timed system; Stochastic programming; Production management; Imperfect information; Moment problem
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/j.compchemeng.2014.04.012

•Optimization matching for generating scenario trees that reduces under-specification•Data-driven method that does not require strict assumptions on probability distribution.•Two approaches for multi-stage scenario trees based on time series and forecasting.•Application in production planning with uncertain yield and correlated product demands. This paper brings systematic methods for scenario tree generation to the attention of the Process Systems Engineering community. We focus on a general, data-driven optimization-based method for generating scenario trees that does not require strict assumptions on the probability distributions of the uncertain parameters. Using as a basis the Moment Matching Problem (MMP), originally proposed by Høyland and Wallace (2001), we propose matching marginal (Empirical) Cumulative Distribution Function information of the uncertain parameters in order to cope with potentially under-specified MMP formulations. 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 production planning problem with uncertainty in production yield and correlated product demands.