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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