A continuous-time formulation for scheduling multi-stage multi-product batch plants with identical parallel units

Abstract

Multi-stage multi-product batch plants with parallel units are quite common in the batch chemical industry. How to assign products to those units optimally have become formidable scheduling problems considering the large number of assignment possibilities. To find a better way to solve these tough problems, we turn to find a way by studying the simplified problems (scheduling of multi-stage multi-product batch plants with identical parallel units) first. Instead of deciding the product sequence on each unit, we focus on the sequence of products at the start time and end time of each stage. Each stage is considered as a 'black box' in which we care about which time and who will enter and leave these 'black boxes' and need not care about how these 'black boxes' perform. We develop MILP formulations based on this idea. Examples show that formulations with this idea have a great reduction in binary variables and non-zero elements compared to the slot-based formulations existing in the literature. Finally, we find one formulation within the three formulations developed by us performs best comparing with the formulations in the literature.