中文摘要：

个性化产品的生产过程具有非重复性,致使工序的加工时间不确定且难以估计其概率信息。因此,传统的确定调度和随机调度方法不再适用。采用最小化最大后悔值的鲁棒优化方法,研究变速平行机加工环境下个性化产品的生产调度问题。首先,采用区间情景描述不确定的加工时间,构建基于后悔值准则的个性化产品鲁棒调度模型;其次,证明任意调度方案带来的最大后悔值可通过求解一个指派问题得到;然后,提出基于混合整数规划和迭代松弛过程的两种精确算法获取最优解;最后,通过仿真实验评估两种精确算法的有效性,结果表明基于混合整数规划的精确算法明显优于迭代松弛算法,并且可以快速求解中小规模的调度问题。

英文摘要：

The production process of personalized products is non-repetitive, which leads to the uncertainty of job processing times and the difficulty to estimate their probability information. Thus,the classical deterministic or stochastic scheduling approaches are unsuitable. A rain-max regret robust optimization approach was used to study the production scheduling problem of personalized products with unrelated parallel machines. Firstly, a robust scheduling model with regret criterion was developed for the personalized products and the uncertain processing times are modeled by interval scenarios. Secondly, it was proved that the maximal regret for any schedule can be obtained by solving an assignment problem. Then, two exact algorithms based on mixed integer program and iterative relaxation procedure were proposed to get the optimal solutions. Finally, simulation experiments were conducted to evaluate the effectiveness of the two exact algorithms. The results show that the exact algorithm based on mixed integer program significantly outperforms the iterative relaxation algorithm, and can solve the small and medium-sized scheduling problems quickly.