Novel continuous-time formulations for scheduling multi-stage multi-product batch plants with identical parallel units

Scheduling production optimally in multi-stage multi-product plants is a very difficult problem that has received limited attention. While the case of non-identical parallel units has been addressed, the case of identical parallel units is equally worthy of attention, as many plants are or can be approximated as such. In this paper, we construct and compare several novel MILP formulations for the latter. In contrast to the existing work, we increase solution efficiency by considering each stage as a block of multiple identical units, thereby eliminating numerous binary variables for assigning batches to specific units. Interestingly, a novel formulation using an adjacent pair-wise sequencing approach proves superior to slot-based formulations.