Simultaneous Batching and Scheduling in Multistage Multiproduct Processes

In this article, we present a mixed-integer programming formulation for the simultaneous batching and scheduling in multiproduct multistage processes. The proposed sequence-based formulation addresses limitations of existing approaches where batching and scheduling decisions are carried out sequentially. To account for batching decisions, we use additional batch-selection and batch-size variables and introduce demand-satisfaction and unit-capacity constraints. Assignment constraints are active only for the subset of batches that are selected, and sequencing is carried out between batches that are assigned on the same processing unit. We also propose an alternate formulation to handle sequence-dependent changeover costs. Finally, to enhance the computational performance of the model, we present methods that allow us to fix a subset of sequencing variables and we develop a class of tightening inequalities based on time windows.