Sets formulation to schedule mixed batch/continuous process plants with variable cycle time

Effective scheduling of operations in the process industry has the potential to achieve high economic returns. Process plants containing both batch and continuous units present a difficult scheduling problem. When these processes are modelled with batch cycle times as decision variables, the complexity of the problem is increased significantly. These problems when modelled in the conventional MILP formulation, are extremely difficult to solve as they are NP-hard. Many solution methods require unacceptable amounts of time/memory to solve even a simple problem. A formulation based on the set-covering principle that constructs feasible sub-schedules is considered. Modelling considerations, such as identifying and generating sub-schedules are discussed. The motivation for this work is an existing scheduling problem in the sugar milling industry. A smaller problem, which contains the important characteristics of the sugar milling problem, is initially considered for performance comparison. A substantial reduction in the complexity required to solve the problem is achieved using the sets formulation. The sets implementation is then applied to a sugar mill scheduling case study. It is found that the method is able to return objective function values 45% better than current industry practice. Conventional MILP approaches are unable to solve this larger case study.