A novel continuous-time MILP formulation for multipurpose batch plants. 1. Short-term scheduling

In this paper, a new concept, the so-called state sequence network representation, is presented. This representation is based on states only, eliminating the use of tasks and units. Using this new representation as a basis, a novel continuous-time MILP formulation for short-term scheduling of multipurpose batch plants is developed. The presented formulation can readily be extended to intermediate due date scenarios. Also presented in this paper is a new model for the duration constraints that explores degrees of freedom that are intrinsic in batch operations. These are due to operator intervention, raw material purity, and different catalyst types. Time points are used to denote the use or production of a particular state. This formulation leads to the least number of binary variables and much better results when compared to other continuous-time formulations published in the literature. The reduced number of binary variables is a result of considering states only, thereby eliminating binary variables corresponding to tasks and units. This method has been applied to literature examples and industrial problems which show significant improvement in reducing the number of binary variables and, hence, CPU times. The last section of this paper introduces the concept of units aggregation in reducing the binary dimension of large-scale problems. This makes it possible for the method to solve large-scale industrial problems. In the second paper of this series (Zhu, X. X.; Majozi, T. Ind. Eng. Chem. Res. 2001, 40, 5621-5634), it will be demonstrated how this formulation is applied in the context of integrated planning and scheduling.