以典型的冷轧生产系统为研究背景，针对具有高附加值的O5产品的集批生产计划问题进行了研究。由于此类产品对表面质量的要求极高，导致其生产过程中涉及的切换费用和库存成本非常高。鉴于此，以最小化切换费用和库存成本为目标建立了用于描述O5产品集批生产计划问题的混合整数规划模型，模型中充分考虑了各种实际相关约束。同时开发了有效的拉格朗日松弛求解算法，并使用基于实际生产数据产生的400个算例进行了仿真实验，计算结果显示该算法能够在合理的时间内得到高质量的解。

Taking a typical cold rolling production system as the research background, the batch production planning problem for high-value-added O5 products is studied. Due to the extremely high surface quality requirements of these products, the associated setup costs and inventory costs in the production process are significantly high. In light of this, a mixed-integer programming model is formulated to describe the batch production planning problem for O5 products, aiming to minimize setup costs and inventory costs with full consideration of practical technological constraints. Additionally, an effective Lagrangian relaxation approach is proposed to solve the problem. A numerical experiment composed of 400 instances is designed based on actual production data. Computational results prove that high quality solutions could be found in a reasonable time.