A Multi-Level Algorithm for Production Scheduling and Sequencing Optimization in Hot Rolling Steel Mills

Abstract

The objective of the hot rolling mill is to transform slabs of steel into thin strips which conform to specific dimensional and metallurgical customer requirements. High performance and flexibility in the operation is required due to strict customer demands, variable market conditions, and the drive for continuous improvement. Historically human schedulers have performed the scheduling and sequencing tasks, however it is not a reasonable expectation that they consider all the complex objectives required in optimal production of a hot mill. Therefore, there are significant opportunities for improvement in this area through the application of mathematical optimization models and solution algorithms. This work presents a set of models and a solution algorithm for optimal scheduling and sequencing of production within a hot rolling steel mill. The models and algorithms presented within this thesis are specifically developed for ArcelorMittal Dofasco’s Hot Strip Mill in Hamilton, Ontario, Canada. First, a graph theoretic representation of the production block is developed along with an asymmetric travelling salesman formulation of the sequencing problem. A slab transition cost function comprised of the hot rolling process objectives is formalized. The objective of the optimization is to generate a complete block sequence which minimizes the cost of transitions between slabs thus minimizing the overall cost of production. The Concorde exact solver is leveraged for the sequencing problem. Second, the scheduling of slabs from inventory into blocks is considered in addition to sequencing. A methodology for slab clustering is defined. The novel concept of width-groups is developed and a heuristic algorithm is devised to calculate an objective for the MILP slab scheduling model. The objective of the scheduling optimization is to construct a set of blocks which minimize deviation from the calculated width-group design. A revised sequencing model, updated to reflect the relaxations enabled by the width-group design, is formulated. Industrial production and offline trials show that the proposed scheduling-sequencing framework outperforms the human scheduler in all critical performance metrics for both scheduling and sequencing. A conservative estimate of the reoccurring monetary benefits available from use of the proposed scheduling-sequencing optimization framework is greater than $1.2M CAD per year.