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

<p>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.</p

Hybrid Bilevel-Lagrangean Decomposition Scheme for the Integration of Planning and Scheduling of a Network of Batch Plants

<p>Motivated by a real-world industrial problem, this work deals with the integration of planning and scheduling in the operation of a network of batch plants. The network consists of single-stage, multiproduct batch plants located in different sites, which can exchange intermediate products in order to blend them to obtain finished products. The time horizon is given and divided into multiple time periods, at the end of which, the customer demands have to be exactly satisfied. The planning model is a simplified and aggregate formulation derived from the detailed precedence-based scheduling formulation. Traveling Salesman Problem (TSP) constraints are incorporated at the planning level in order to predict the sequence-dependent changeovers between groups of products, within and across time periods, without requiring the detailed timing of operations, which is performed at the scheduling level. In an effort to avoid solving the full-space, rigorous scheduling model, especially for large problem sizes, two decomposition strategies are investigated: Bilevel and Temporal Lagrangean. We demonstrate that Bilevel Decomposition is efficient for small to medium problem instances and that further decomposition of the planning problem, yielding a hybrid decomposition scheme, is advantageous for tackling a large-scale industrial test case.</p