基于拉格朗日下界求解的炼钢-连铸生产调度方法

为提高炼钢-连铸生产效率,以加权总完工时间、作业等待惩罚总和最小化为目标,基于时间索引建立数学规划模型。在证明原问题、松弛问题、对偶问题三者最优解关系基础上,将机器容量约束松弛到目标函数中,运用次梯度算法求原问题下界,得到各炉次的开始时间序列。为消除松弛解中的有向环,采用融入启发式规则的列表调度,按照机器可用性优先原则,将炉次均衡地指派到各个加工机器上。利用GAMS/Cplex软件对18个调度算例进行测试运算,结果表明以较少的计算代价可以得到令人满意的近优解,因此本文提出的基于拉格朗日下界求解的方法对炼钢-连铸生产调度问题是可行的和有效的。

Lagrangian lower bound solution based method for steelmaking-continuous casting production scheduling

To improve the production efficiency of steelmaking-continuous casting, a mathematical programming model is established based on time index with the objective of minimizing the sum of weighted completion time and waiting punishment. with the relationship between the optimal solutions of original problem, relaxation problem and dual problem proved, the machine capacity constraints are relaxed to the objective function, and the sub-gradient method is employed to seek the lower bound of the original problem, then the start time sequence of all ladles is obtained. To eliminate the directional ring in the relaxation solution, a list scheduling method integrated with heuristic rules is used and all ladles are evenly assigned to the machines according to the priority principle of machine availability. Eighteen scheduling examples are calculated by GAMS/Cplex software. The results show that satisfactory near optimal solution can be achieved at less computing cost. So the proposed method based on Lagrangian lower bound solution is feasible and effective to solve the steelmaking-continuous casting production scheduling problem.