Redefining event variables for efficient modeling of continuous-time batch processing

We define events so as to reduce the number of events and decision variables needed for modeling batch-scheduling problems. We propose a new mixed integer linear programming formulation based on this concept, defining non-uniform time periods as needed and decision variables that are not time-indexed. It can handle complicated multi-product/multi-stage machine processes, with production lines merging and diverging, and with minimum and maximum batch sizes. We compare it with earlier models and show that it can solve problems with small to medium demands relative to batch sizes in reasonable computer times.