Abstract This research focuses on solving a scheduling problem in a heat treatment line of a multinational steel company. A bi-objective model is proposed to minimize the line total energy costs and total tardiness. The solution is carried out through a matheuristic technique that combines metaheuristics and mathematical programming. A Mixed Integer Linear Programming (MILP) model is designed to generate initial solutions to a Multi-objective Variable Neighborhood Search (MOVNS) algorithm. One benefit of this approach is the ability to handle large-scale problems, common in real production scheduling cases, with reasonable computational time and alternative quality planning. The suggested matheuristic is proven to be statistically superior to an only metaheuristic approach, taking as performance metric the final approximated Pareto solutions’ hypervolume. Tests performed with data from the industry showed improvements in the scheduling of the heat treatment line with reductions of energy costs and tardiness up to 13% and 90%, respectively. The methodology can also be extended to other similar scheduling processes.

中文翻译：

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钢铁工业热处理线总延迟和能源成本最小化的多目标数学算法

摘要 本研究的重点是解决某跨国钢铁公司热处理生产线的调度问题。提出了一个双目标模型来最小化线路总能源成本和总延误。该解决方案是通过一种结合了元启发式和数学编程的数学式技术来实现的。混合整数线性规划 (MILP) 模型旨在生成多目标变量邻域搜索 (MOVNS) 算法的初始解。这种方法的一个好处是能够以合理的计算时间和替代的质量计划处理大规模问题，这在实际生产调度情况下很常见。所建议的数学方法被证明在统计上优于唯一的元启发式方法，将最终近似的帕累托解的超体积作为性能指标。使用行业数据进行的测试表明，热处理线的调度得到了改进，能源成本和延迟分别降低了 13% 和 90%。该方法还可以扩展到其他类似的调度过程。