Scheduling model for a multi-product batch plant using a pre-ordering approach

A scheduling model for a multi-product, multistage batch plant with parallel units is presented. The objective is to maximize the weighted completion times of orders in every processing stage while imposing a penalty on the slower orders. The proposed model uses the continuous-time representation mode and describes the allocations of tasks, units and stages by a set of binary variables. In order to reduce the model size and provide a more effective solution to the model, a pre-ordering approach that sorts the processing sequence of orders is developed. The pre-ordering approach identifies the infeasible assignments through which the number of binary variables is significantly reduced. Illustrative examples are provided to show that the size of the proposed model is small, and therefore, needs much less computational effort in comparison with the existing models in the literature.