An Improved MILP Formulation for Scheduling Multiproduct, Multistage Batch Plants

Many multiproduct batch plants in the chemical industry employ multiple stages of nonidentical parallel units and operate on the basis of customer orders with different delivery dates. In this work, we present a new continuous-time mixed integer linear programming formulation without using time slots for the short-term scheduling of such plants. Our formulation allows both sequence-dependent and unit-dependent setup times and common operational considerations such as initial plant state and order/unit release times. We develop several novel constraints for the assignment of consecutive orders on a single unit and evaluate them thoroughly to identify the best constraints. Finally, we solve several examples to demonstrate the superiority of our proposed formulations. In comparison to existing works, our formulation requires roughly 30% fewer constraints, yields superior schedules, and reduces the computational times by 65%. We highlight the impact of M in big-M constraints on solution times and propose an industrially more realistic and computationally more efficient (99.8% reduction in solution time) scheduling objective of minimizing tardiness.