two reheat  furnaces. When slabs are at the right  tempera-
ture,  they  can be rolled  one by one on the roughing  mill and
then  on  the  finishing mill.  Reheat  furnaces work  in  a
continuous way, like pushers.  Their goal is to create  a roll
life (sequence  of slabs)  to be processed  on the finishing  mill
with minimum  penalties  associated  with production  quality,
while  ensuring  on-time  deliveries  and  increased  productivity.
The penalties  take into account  factors  similar  to ours like
width,  gauge  and  hardness transitions. They  also  have
different  priority  classes for  the  orders. The authors first
develop  a mathematical  model  for their  problem,  which  can
be seen as a generalization  of  the PCTSP  (Prize Collecting
Travelling Salesman Problem). Then,  a  new  idea  called
'cannibalization'  is introduced.  Basically,  the authors  create
several solutions with  different slabs and  combine good
pieces  taken  from  each  sequence  to  generate  better
sequences. Different greedy heuristics are used  to  create
starting  solutions, which are then improved with a  short
tabu  search. After the cannibalization  phase, longer tabu
searches are  performed to  get  the  final  solutions. The
problem  is similar  to ours  because  pieces  need  to be selected
and sequenced  on the mill. On the other hand,  they do not
need  to  create blocks  or  batches  for  heating purposes
because  continuous  furnaces  are used.
Cowling  and Rezig  (2000)  propose  a heuristic  algorithm  to
solve a hot  strip mill planning  problem. The solution also
integrates synchronization  between the  continuous caster
that  produce slabs and  the mill. However, they do  not
mention homogenizing  furnaces  to  heat  slabs before hot
rolling. Their mill  is  characterized  by  very  strict width
transitions and  hardness constraints. A  system of  wear
points  is  used  to  estimate roll wear. The  objective
is  to
maximize  the  'score'  of a schedule,  where  the  latter  takes  into
account  different factors  like  due  date  and  production
quality.  The authors  propose  a mixed  integer  formulation  of
the  problem. Their problem-solving  approach iteratively
fixes the values of  the integer  variables  to  obtain network
flow subproblems  that can be efficiently  solved.
In  the  work  of  Dupont  et  al  (1997),  simple  greedy
heuristics  are  proposed  to schedule  a steel  rolling  mill. More
sophisticated heuristic approaches, in  particular genetic
algorithms  (GA), have also been applied to  this kind of
scheduling  problems.  Fang and Tsai  (1998)  describe  a GA to
solve a  steel hot  strip mill scheduling  problem with width
transitions constraints  ('coffin  shapes')  and  roll  wear.
Tamaki  et  al  (1994)  develop  an  algorithm to  schedule furnaces  and a mill in a  steel hot rolling process. To deal 启发式算法热轧机铝英文文献和中文翻译(5):http://www.youerw.com/fanyi/lunwen_16688.html