Continuous annealing is a core process in steel cold-rolling facilities. It is used to set desired material properties by passing coils of flat steel through a high-temperature furnace in a precisely controlled manner. High efficiency is achieved by feeding the steel through the furnace in the form of a continuous strand. For this purpose, the coils are welded together before being fed into the furnace. Whenever two consecutive coils are incompatible, a special dummy coil called stringer is used to connect them, which reduces efficiency and adds costs and emissions. We consider the scheduling of coils with specific due dates and alternative order-specific processing modes on parallel heterogeneous lines. The problem is to simultaneously assign coils to lines and sequence them on these lines with a defined processing mode with adherence to tardiness constraints while minimizing the number of stringers needed. To address this problem, we formulate a mixed-integer linear program based on a model from the literature and propose a two-phase heuristic solution procedure. The procedure combines an opening phase using shortest path algorithms and local search with an improvement phase based on problem-specific decompositions according to the principles of an Fix-and-Optimize procedure. The results show that our heuristic outperforms a state-of-the-art commercial solver in finding good solutions in short computation time. Based on a sensitivity analysis for several industry-inspired data sets, we observe a trade-off between efficiency and tardiness which strongly depends on the operating conditions.

中文翻译：

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具有替代处理模式的并行连续退火线的调度，以在延迟约束下优化效率

连续退火是钢材冷轧设备的核心工序。它用于通过将扁钢卷以精确控制的方式穿过高温炉来设定所需的材料特性。通过将钢以连续钢坯的形式送入熔炉，实现了高效率。为此，线圈在送入熔炉之前被焊接在一起。每当两个连续线圈不兼容时，就会使用一种称为纵梁的特殊虚拟线圈来连接它们，这会降低效率并增加成本和排放。我们考虑在并行异构生产线上对具有特定到期日和替代订单特定处理模式的卷进行调度。问题是同时将线圈分配到生产线，并使用定义的处理模式在这些生产线上对它们进行排序，遵守延迟约束，同时最大限度地减少所需的纵梁数量。为了解决这个问题，我们根据文献中的模型制定了混合整数线性程序，并提出了两阶段启发式求解过程。该过程将使用最短路径算法和局部搜索的开放阶段与根据修复和优化过程的原理基于特定问题分解的改进阶段相结合。结果表明，我们的启发式算法在短时间内找到良好的解决方案方面优于最先进的商业求解器。基于对几个行业启发的数据集的敏感性分析，我们观察到效率和延迟之间的权衡，这在很大程度上取决于操作条件。