Abstract: This paper derives production batch scheduling problem from the steelmaking process which is characterized by high temperature, large energy consumption and complex production process. The jobs are given in families according to their production requirements. The concerned problem is to form the slabs into batch and decide the slab schedule, in order to minimize the total production costs including changeover costs between two slabs, and earliness and tardiness penalties. Then the production costs can be reduced, the production quality can be improved. For the problem, a mathematical programming model is formulated based on simulation optimization idea, with consideration of the uncertain processing time and production requirements. Based on the Strong Law of Large Number(SLLN), the model is approximated. Then the sample average approximation framework is proposed, where different sample are obtained by randomly sampling, filter and fan algorithm is proposed to solve the deterministic problem in each sample. Finally, the efficiency of the proposed algorithm is evaluated by the computational experiments based on practical data.

Key words: batch scheduling, sample average approximation, filter &, fan

摘要： 论文针对钢铁企业炼钢工序具有高温、高能耗、复杂工况的实际特征,从中提炼出生产批调度问题,其工件根据其实际工艺属性可分为多个簇,基于给定的工件簇,决策工件的分批和调度情况,综合考虑工件之间的切换费用,以及工件提前、拖期所导致的惩罚,使得总的生产成本期望最小化,从而降低生产成本;针对该问题,考虑工件的处理时间、工件的加工属性具有不确定性,基于仿真优化思想,建立数学模型,并基于大数定理,对模型目标函数进行近似;提出基于样本近似方法的求解框架,通过随机抽样的方法获得不同规模的样本,针对不同规模的样本,提出Filter & Fan算法对问题进行求解;最后,通过基于实际数据的计算实验验证所提算法的有效性。

关键词: 批调度, 样本平均近似, Filter &, Fan