Improving unit-specific event based continuous-time approaches for batch processes: Integrality gap and task splitting

In this work, we address a challenging issue in the area of batch processing scheduling, namely the ability to reduce or even close the integrality gap for large-scale scheduling problems. Because of the multipurpose and multiproduct characteristics of batch plants, their resulting scheduling problems can be highly combinatorial in nature with many variables and constraints. In order to help reduce this complexity, a number of preprocessing steps are performed and new sets of rigorous constraints are incorporated within a novel and effective continuous-time formulation for the short-term scheduling of batch plants. Several example problems are solved to demonstrate the effectiveness of the proposed algorithmic techniques. In addition, a new rigorous mathematical model is proposed to help reduce the complexity experienced in unit-specific event based, continuous-time formulations. A challenging benchmark problem involving several complicating features is solved for several demand instances in order to further demonstrate the effectiveness of the proposed approach.