Hot Mill Scheduling

We developed a hot strip mill scheduling system. We adopted a coarse-to-fine approach for the problem: solving global hard constraints first, and improving the solution quality later. Finally the system automatically generates a better schedule than human scheduling experts, who need more than ten years training, do.

Hot strip mill process is the first rolling process for producing thin coils after steel making, where a slab, a thick (250~270mm) rectangle plate of steel, is rolled into a thin (1.2~8mm) coil under very high temperature and pressure. Because of the wear of roller surface the rollers are replaced periodically and a sequence of slabs between the roller changes are called a round. The scheduling problem for the hot strip mill is to determine several rounds from a given slab pool (a set of available slabs to schedule) at a time. Most of the constraints considered in sequencing slabs come from the rolling condition of a roller. Higher temperature and pressure required to produce thinner coil gradually damage the rolling condition, so we need to avoid too long consecutive rolling of thin coils and insert thicker coils for recovering the rolling condition.

Fig.1 - Hot strip mill process in coil production process flow

We can regard hot strip mill problem as a mixture of a knapsack problem, a constraint satisfaction problem, and a traveling salesperson problem.

• Knapsack problem (slab selection): we need to select appropriate subsets of slabs for rounds from a slab pool in order to balance the quality of rounds and maximize the usage of rollers.
• Constraint satisfaction problem (global constraints): constraints on slabs apart in a round such as mixture and precedence between subsequences of thin coils, earlier positioning of high surface quality slabs, and minimum requirement of recovery slabs between thin coils must be satisfied.
• Traveling salesperson problem (local constraints): constraints between a pair of adjacent slabs must be satisfied and transition of attribute values such as band width, band gauge, temperature, and tensile should be as smooth as possible.

Historically in the literature the aspects of knapsack problem and traveling salesperson problem are emphasized in the scheduling algorithm. However, if the ratio of thin coils, which must satisfy strong global constraints, in a slab pool is relatively high, it makes the scheduling problem more difficult.

The challenge of the project is to find a feasible and near optimal schedule within a practical time (less than half an hour). The quality of a round depends mostly on the selection of thin coils. Therefore we focus on the selection of thin coils and have taken coarse-to-fine approach to build two or three rounds in four steps.

1. Clustering: as a preprocessing, we make greedily a small subsequence (cluster) of slabs satisfying some local constraints. Within a subsequence, mixture and precedence relation of thin coils are also satisfied.
2. Rough sequencing: we determine a block pattern of slab clusters, which reflects typical pattern of a round; special surface quality coils and three iterations of thin coils and thick coils. We formulated an assignment problem of slab clusters to a block pattern as integer programming. Slab selection and some of global constraints are solved in this phase.
3. Detail sequencing: we complete initial feasible solution by inserting slabs between slab clusters selected in rough sequencing. Both global and local constraints are solved in this phase.
4. Local improvement: we applied local search operations (insert, delete, and exchange slabs) in order to improve the length of rounds and the smooth transition of slab attributes involved in local constraints.

By solving key global constraints in rough sequencing phase, we could obtain a promising skeleton of a round leading to a better schedule, and restrict the search space in an effective way. As a result, in shorter time and without any post manual editing, the scheduling system generates, in most cases, feasible and longer rounds competitive to ones generated by a human scheduling expert.

Fig.2 - Coarse to fine approach to hot strip mill scheduling