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2.3. Orders
Ingots are grouped into orders. Each order is made of one
or more ingots with the same specifications. An order is
characterized by
* an order ID,
* a number of ingots,
* an alloy code,
* a product code,
* initial dimension (before hot rolling): thickness, width and
length,
* final dimension (after hot rolling): gauge and width,
* a homogenization code,
* a due date.
As much as possible, ingots from the same order should
be in the same batch and should be processed consecutively
on the mill. We call each batch a block, and the orders in a
block are sequenced according to their processing order on
the hot mill. All ingots in a block must be rolled before
another block can be processed on the same furnace and on
the mill.
The due dates are handled indirectly by defining three
different categories of orders: late, rush and normal. A late
order is already late; a rush order has to be scheduled during
the current roll life to avoid lateness; the remaining orders
are normal.
2.4. Solutions
A solution to our problem corresponds to a sequence of
blocks on the rolling mill that satisfies all hard constraints
(and from which the sequences on the furnaces can be
deduced). A solution also indicates the scheduling of each
operation on the mill and furnaces.
3. Literature review
Specific literature on this type of problems is scarce.
However, there are a little bit more publications for steel
than for aluminum. In the aluminum domain, Stauffer and
Liebling (1997) describe a problem similar to ours. Three
furnace types are considered: pusher, large soaking pit and
small soaking pit. To fill the soaking pits with minimum
residual capacity, a bin-packing problem is solved. Alloys
are split into groups of similar hardness, and each group has
a wear coefficient and a feasible wear interval on the rolls.
In this application, the rolling mill does not run on a
continuous basis, but is shut down every night and on
Sunday. Also, width transitions are not taken care of. The
objective considers both order tardiness and production
quality (expressed through penalties). To solve this problem,
the authors use a tabu search algorithm. A rough estimate of
the minimum objective value is first calculated to quickly
eliminate poor solutions and speed up the search. A rolling-
horizon approach is also developed to allow daily dynamic
re-scheduling that takes into account new incoming orders
and new priorities.
Lopez et al (1998) describe a tabu search approach to
create hot strip mill production schedules in the steel
industry. Long bars, called slabs, are first heated in one of