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An enhanced continuous-time formulation is presented for the short-term scheduling of multipurpose batch plants with intermediate due dates. The proposed formulation is based on the continuous-time formulation introduced by Ierapetritou and Floudas ( Ind. Eng. Chem. Res . 1998, 37, 4341 and 4360) and incorporates and elaborates on several features that include (i) various storage policies (UIS, FIS, NIS, and ZW), (ii) resource constraints, (iii) variable batch sizes and processing times, (iv) batch mixing and splitting, and (v) sequence-dependent changeover times. The key features of the proposed formulation include a continuous-time representation utilizing a necessary number of event points of unknown location corresponding to the activation of a task. Also, tasks are allowed to continue over several event points, enabling resource quantities to be correctly determined at the beginning of each resource utilization. Several examples are presented to illustrate the effectiveness of the proposed formulation, and comparisons with other approaches are provided.
Janak et al. (Sat,) studied this question.