A Flow Shop with Compatibility Constraints in a Steelmaking Plant

We present a scheduling methodology for applications where the generation of schedules is constrained by antagonistic and vague knowledge. Besides temporal and capacity constraints, compatibility constraints between consecutive jobs are managed. We model the vague constraints and uncertain data by fuzzy set theory. The importance of single jobs and and the difficulty to schedule them is defined on the different constraints and is used to control the generation of schedules. A preliminary schedule is generated by considering the important jobs and those that are difficult to schedule first. Easy or not so important jobs are scheduled later. Finally, the achieved schedule is “repaired” until a schedule is found that achieves a given level of satisfaction. Since the goodness of solutions is rated by fuzzy sets, robust schedules achieve better evaluations than weak schedules. However, if no robust solution is found constraints will be relaxed. This methodology is appropriate for applications in process engineering where uncertain knowledge is dominant. We explain the methodology with a case study from a steelmaking plant for high-grade steel.