The steelmaking and continuous casting (SCC) process is one of the vital processes in iron and steel plants since it determines chemical compositions of slabs and is often a bottleneck for iron and steel manufacturing. In this paper, we first develop a discrete-time mixed-integer linear programming (MILP) formulation for a new SCC scheduling problem where different processing routes are used to produce diversified and personalized slab products. To solve the proposed MILP formulation efficiently, we then propose a novel efficient solution algorithm using Augmented Lagrange multiplier method (e-ALM) through relaxation of the coupling constraints and incorporation of penalty components. A heuristic-based list scheduling approach as well as adjacent pairwise swap operations is used to construct a high-quality feasible schedule. A fine-adjusting strategy based on the subgradient direction is proposed to update Lagrangian multipliers dynamically to speed up the convergence. It is shown that the proposed e-ALM is able to generate optimal or near-optimal solutions with 5% optimality for 150 industrial-scale instances and outperform the commercial solver GAMS/CPLEX and the existing Lagrangian relaxation algorithms with better feasible solutions and smaller duality gap within the specified computational time.

炼钢和连铸（SCC）工艺是钢铁厂中至关重要的工艺之一，因为它决定了板坯的化学成分，并且通常是钢铁制造的瓶颈。在本文中，我们首先针对新的SCC调度问题开发了离散时间混合整数线性规划（MILP）公式，其中使用了不同的加工路线来生产多样化和个性化的板坯产品。为了有效地解决提出的MILP公式，我们然后通过放松耦合约束和引入罚分来提出一种使用增强拉格朗日乘数法（e-ALM）的新颖有效解决算法。基于启发式的列表调度方法以及相邻的成对交换操作用于构造高质量的可行调度。提出了一种基于次梯度方向的精细调整策略，可以动态更新拉格朗日乘子，以加快收敛速度​​。结果表明，所提出的e-ALM能够针对150个工业规模实例生成5％最优性的最优或接近最优解，并且优于商用解算器GAMS / CPLEX和现有的拉格朗日松弛算法，具有更好的可行解和较小的对偶性指定计算时间内的间隔。