Batch process scheduling with es-graph: a case study

Abstract

The scheduling of batch processes is a widely researched field of chemical engineering. Over the last few decades, a great number of tools have been developed for industrial examples and literature problems. These methods vary not only in their applied model, but in their representation of the problem inputs as well. The most well-known representations are the State-Task Network, the Resource-Task Network, the State Sequence Network, and the S-graph. While the latter also serves as the mathematical model for the related optimization approaches, the others only act as an intermediate model between the raw problem data and the model used for optimization, e.g., a mixed-integer linear programming model. The eS-graph model is a generalization of the S-graph, where the one-to-one relation between nodes and tasks has been relaxed, allowing a much wider range of scheduling problems to be tackled. Processes may simultaneously occupy several units, and release them at different stages of execution, and certain stages of separate processes can be forced to overlap in time. As in the case of the S-graph, the eS-graph models can be solved to optimality by specially designed combinatorial algorithms or serve as a basis for precedence based linear programming formulations. In this work, the modelling capacities of the eS-graph framework are illustrated via a Polymer production case study, where complex timing constraints are present.