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 启发式算法热轧机铝英文文献和中文翻译(4):http://www.751com.cn/fanyi/lunwen_16688.html