Integrated Sequencing and Scheduling in Coil Coating

We consider a complex planning problem in integrated steel production. A sequence of coils of sheet metal needs to be color coated in consecutive stages. Different coil geometries and changes of colors necessitate time‐consuming setup work. In most coating stages one can choose between two parallel color tanks. This can either reduce the number of setups needed or enable setups concurrent with production. A production plan comprises the sequencing of coils and the scheduling of color tanks and setup work. The aim is to minimize the makespan for a given set of coils. We present an optimization model for this integrated sequencing and scheduling problem. A core component is a graph theoretical model for concurrent setup scheduling. It is instrumental for building a fast heuristic that is embedded into a genetic algorithm to solve the sequencing problem. The quality of our solutions is evaluated via an integer program based on a combinatorial relaxation, showing that our solutions are within 10% of the optimum. Our algorithm is implemented at Salzgitter Flachstahl GmbH, a major German steel producer. This has led to an average reduction in makespan by over 13% and has greatly exceeded expectations.