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1. Introduction In a standard rolling plant there are three main shops, the foundry, the hot line and the cold line. In the foundry, recycled pieces of aluminum are melted in large furnaces. During this operation, different elements like magnesium or zinc are added to the mixture to obtain a specific alloy. Afterwards, the metal in liquid form is poured into a casting pit to produce ingots. Different dimensions are obtained by changing the casting table. When ingots are solidified and cooled, they are transferred to the hot line. First, they are scalped to eliminate impurities that tend to accumulate on the edges. Then, ingots are heated in homogenizing furnaces to obtain desired mechanical properties and to prepare them for the next operation, where they are rolled in a hot mill at near 6000C. This operation reduces their thickness to a fraction of an inch and produces long sheet coils. In the cold line, coils are processed by different machine centers, like the cold mill, annealing furnaces, and tension leveller to obtain their final desired properties. The sequence of operations often depends on the product and can change in course of operations, as different sequences are equivalent. In this paper, we focus on the hot line, in particular the homogenizing furnaces and the rolling mill. A good synchronization between the furnaces and the mill is very important because any waste time on the hot mill is costly in terms of productivity and energy savings (as the mill must be maintained at the right temperature). On the other hand, the production must satisfy quality standards. Therefore, a good trade-off between quality and efficiency must be found. To complicate the matter, the process imposes specific 23562
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constraints on the solution. Some must absolutely be
satisfied (hard constraints), while others can be relaxed by
adding penalties to the objective (soft constraints, prefer-
ences). The goal is to find a good compromise among these
conflicting objectives, while satisfying hard constraints.
The following Section 2 describes the problem under
study. Then, a short literature review is presented in Section
3, followed by a description of our heuristic algorithm in
Section 4. Numerical results are reported in Section 5.
Finally, the conclusion is presented in Section 6.
2. Problem description
In a standard rolling plant, ingots are casted in the foundry,
rolled into coils on the hot line and then rolled at room
temperature on the cold line. The hot line contains two main
machine centres: one with the homogenizing furnaces and the
other with the mill, in that order. They are described as follows:
2.1. Homogenizing furnaces
The goal of homogenization is to thermically treat ingots to
obtain desired mechanical properties and to have them at the
right temperature for the hot rolling operation that follows.
The heating time varies a lot and can take between 10 and
50 h, depending on the homogenization code and furnace
type. Each ingot has its own code and all codes in a batch
must be compatible. The code with the longest duration
determines the batch code and the heating time. Although
this is not ideal, ingots can also be kept longer in the furnace
as long as a predefined maximum time associated with each