Proposed by Ian Miguel

Specification - Type 1

Steel is produced by casting molten iron into slabs. A steel mill can produce a finite number, σ, of slab sizes. An order has two properties, a colour corresponding to the route required through the steel mill and a weight. Given d input orders, the problem is to assign the orders to slabs, the number and size of which are also to be determined, such that the total weight of steel produced is minimised. This assignment is subject to two further constraints:

1. Capacity constraints: The total weight of orders assigned to a slab cannot exceed the slab capacity.
2. Colour constraints: Each slab can contain at most p of k total colours (p is usually 2).

The colour constraints arise because it is expensive to cut up slabs in order to send them to different parts of the mill.

The above description is a simplification of a real industrial problem (see [1]). For example, the problem may also include inventory matching, where surplus stock can be used to fulfil some of the orders.

Specification - Type 2

The Type 1 specification does not constrain the number of slabs used. The Type 2 specification (see [2]) extends the objective to require further that the number of slabs used to accommodate the minimal weight of steel is also minimised.

1. J. R. Kalagnanam, M. W. Dawande, M. Trumbo, H. S. Lee. “Inventory Matching Problems in the Steel Industry,” IBM Research Report RC 21171, 1998.
2. A. Gargani, P. Refalo. An Efficient Model and Strategy for the Steel Mill Slab Design Problem. Proceedings of the 13th International Conference on Principles & Practice of Constraint Programming, 77-89, 2007.