prob038: Steel Mill Slab Design
Specification
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:
- Capacity constraints: The total weight of orders assigned to a slab
cannot exceed the slab capacity.
- 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.
- J. R. Kalagnanam, M. W. Dawande, M. Trumbo, H. S. Lee.
"Inventory
Matching Problems in the Steel Industry,"
IBM Research Report RC 21171, 1998.
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