A novel framework for the identification of complex feasible space

Feasibility analysis is suitable to determine the combinations of input parameters that satisfy all operating and quality constraints, i.e., the process design space. In the presence of disjoint feasible regions and for computationally expensive/nonconvex problems, the use of surrogate-based approaches has been increasingly adopted. However, the choice and prediction accuracy of a suitable surrogate depend on the process of interest, and on the available dataset. In this study, we propose a novel workflow which combines different mathematical tools to (i) investigate how to identify the process feasible space relying on the available training dataset, (ii) assess whether there is a minimum number of sampling points that are necessary to uncover the complexity of the original feasibility function, and (iii) support proper surrogate model selection, while improving accuracy. The proposed methodology is tested on analytical problems and a pharmaceutical process, showing its effectiveness in the identification of complex feasible regions

Effective Continuous-Time Formulation for Short-Term Scheduling: I. Multipurpose Batch Processes

During the last decade, the problem of production scheduling has been realized to be one of the most important problems in industrial plant operations especially when multipurpose/multiproduct batch processes are involved. This paper presents a novel mathematical formulation for the short-term scheduling of batch plants. The proposed formulation is based on a continuous time representation and results in a Mixed Integer Linear Programming (MILP) problem. The novel elements of the proposed formulation are (i) the decoupling of the task events from the unit events, (ii) the time sequencing constraints, and (iii) its linearity. In contrast to the previously presented continuous-time scheduling formulations, the proposed approach leads to smaller and simpler mathematical models which exhibit fewer binary and continuous variables, have smaller integrality gaps, require fewer constraints, need fewer linear programming relaxations, and can be solved in significantly less CPU time. Several exa..