On the solution of large-scale mixed integer programming scheduling models

In this paper, we show how four recently developed modeling and solution methods can be integrated to address mixed integer programs for the scheduling of large-scale chemical production systems. The first method uses multiple discrete time grids. The second adds tightening constraints that lower bound the total production and number of batches for each task and material based on the customer demand, while the third generates upper bounding constraints based on inventory and resource availability. The final method is a reformulation that introduces a new integer variable representing the total number of batches of a task. We apply the aforementioned methods to large-scale problems with a variety of processing features, including variable conversion coefficients, changeovers, various storage policies, continuous processing tasks, setups, and utilities, using a discrete-time model. We illustrate how these methods lead to significant improvements in computational performance.