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Abstract:
The production-scheduling problem has gained considerable importance over the last decade, especially for batch processes due to their inherent flexibility. It is a well-known fact that a good production schedule has a significant impact on the process economics. Extensive research has been done in this area and several elegant approaches have been proposed so far. Most of the approaches reported in the literature till now are based on standard production recipes, i.e. the recipes are standardised either empirically or via single batch optimisation and the information obtained thereby is used for the scheduling problem formulation. However, standardisation of recipes removes degrees of freedom from the system, and due to this scheduling formulations based on standardised recipes result only in suboptimal solutions. This paper presents an overall optimisation approach for the short-term scheduling of batch processes. In the proposed approach, the process dynamics are incorporated within the scheduling formulation rather than being standardised offline. This restores the additional degrees of freedom of the system and can therefore yield a better solution. The proposed formulation is based on a continuous time representation and results in an infinite dimensional mixed integer dynamic optimisation (MIDO) problem. Appropriate discretisation of the control and the state variable profiles transforms this infinite dimensional MIDO problem to a finite dimensional mixed integer non-linear programming (MINLP) problem, which can be approached using conventional MINLP solvers. The effectiveness of the proposed formulation is illustrated with the help of simple examples. The results are compared with the existing scheduling formulations to demonstrate that the proposed approach clearly outweighs the standard recipe approaches.
