通过数字化、智能化手段推进生产制造系统的运营管理优化，提升核心竞争力，关乎企业的长期生存和发展。当今时代外部环境多变，诸如新冠疫情等此类不可预测的事件给企业生产经营带来了不确定性，在管理过程中如果不加以考虑，不合理的决策有可能经过多个环节传导，影响到生产系统整体的正常运转，甚至造成中断、订单交货延期等，给企业造成较大的损失。此外，生产工艺为模型增加了非凸约束，在考虑不确定性时使得相关问题的求解更具挑战性。 本文分别研究了流程型生产行业、离散型制造行业中在不确定条件下并行工作的异质设备调度问题，考虑了生产制造过程的详细非凸工艺约束，针对处于系统关键工序中的非等同并行机，建立了鲁棒优化模型及设计了相应的估计及加速算法，以在不确定参数概率分布信息难以获知时，保证最坏情况下的系统表现不至太差。已有相关领域运用鲁棒优化方法的文献大多忽略了生产工艺约束或者对其进行了较大的简化，使得这些相关的研究方法无法直接应用于实际的场景中指导生产实践。 首先，本文首次将两阶段鲁棒优化模型运用于考虑详细非凸工艺约束的某流程生产设备运营优化问题中，通过分段线性估计及动态规划处理问题的非线性，在运用约束和列生成算法求解时，针对主问题，首次提出对原问题松弛获得解的下界，并通过预判对解空间进行切削的加速算法；针对多维子问题，为了克服在求解高维动态规划时遭遇的“维数灾难”，首次提出了基于邻域搜索和聚合的多维近似动态规划算法，通过推导得出了多维邻域搜索的最小搜索范围。数值实验证明了两种近似加速算法均获得了显著的速度提升。其次，本文首次将基于最小-最大后悔准则的鲁棒优化应用至某离散制造行业非等同并行机调度问题，建立了从产品种类出发的整数线性规划模型，定义了鲁棒松弛模型的悔恨割，经过等价的线性转换，形成了上界收紧的松弛迭代算法。除此以外，基于转移的邻域定义方式和提升当前排程方案需满足的条件，本文设计了局部寻优算法以及禁忌搜索算法对鲁棒模型进行求解。最后，本文研究了某典型离散制造行业非等同并行机在需求不确定下的多品种变批量调度问题，提出了多阶段鲁棒优化模型，基于变量松弛和滚动窗口优化的近似算法、KKT条件及强对偶理论对问题进行了求解和数值验证。文章的最后总结了本文的研究内容和创新点，并提出了未来可能的研究方向。
Operation management optimization of manufacturing system through digital and intelligent methods can enhance the core competitiveness of the enterprises and is crucial to their long-term survival and development. Nowadays the external environment is changeable. Unpredictable events such as Covid-19 have brought uncertainty to production and operation of enterprises. If they are not considered in the management process, unreasonable decisions may transmit through multiple links and affect the normal operation of the entire production system, even cause interruptions, delays in order delivery, etc., causing greater losses to the enterprise. In addition, the process of the production adds non-convex constraints to the model, making the solving of related problems more challenging when considering uncertainty. This paper studies the scheduling problems of non-identical parallel machines under uncertainty in process industries and discrete industries, and considers the detailed process constraints of the manufacturing process. We establish robust optimization models and design corresponding estimation and acceleration algorithms for non-identical parallel machines in key processes of the system, to ensure that the worst-case system performance is acceptable when the probability distribution information of uncertain parameters is difficult to obtain. Most existing literature on robust optimization methods in related fields either ignores the non-convex process constraints that need to be met in complex practical production process, or has simplified the non-convex process constraints, thus these related research methods cannot be directly applied to practical scenarios and guide production practices.First of all, we apply the two-stage robust optimization model in a process production equipment operation optimization problem that considers detailed non-convex process constraints for the first time. The nonlinearity of the problem is dealt with through piecewise linear approximation and dynamic programming. When solving the problem with column and constraint generation algorithm, for the main problem, we relax the original problem and obtain a lower bound, the solution space is cut through pre-judgment. For the multi-dimensional sub-problem, in order to overcome the "curses of dimensionality" encountered in solving high-dimensional dynamic programming, we propose a multi-dimensional approximate dynamic programming algorithm based on neighborhood search and aggregation, and obtain the minimum search range of multi-dimensional neighborhood search through derivation for the first time. Numerical experiments have proved that the two approximate acceleration algorithms both have achieved significant speed improvements. Secondly, we apply robust optimization based on min-max regret criterion to non-identical parallel machine scheduling problem in a discrete manufacturing industry for the first time. We establish a mixed-integer linear programming model based on product category process constraints and define the regret cut for the relaxed robust model. After an equivalent linear transformation, we form a relaxed iterative algorithm with tightened upper bound. In addition, based on a transitional neighborhood definition method and conditions that must be met to improve current scheduling scheme, a local search algorithm and a Tabu Search algorithm are designed to solve the robust model. Finally, we study the lot-sizing and scheduling problem of non-identical parallel machines in a typical discrete manufacturing industry under demand uncertainty and propose a multi-stage robust optimization model. To solve the problem, we propose approximate algorithms based on variable relaxation, rolling horizon, KKT conditions and strong duality theory and numerically verified them. At the end of this paper, we summarize the research content and innovations of this paper and propose possible future research directions.
