Optimal Material Flow Control of Production Lines by Multiscale Network Models

物理模拟、离散模拟、事件模拟或流程模拟是改善生产线物流的模拟方法。这些方法一般适用于单个系统部件的仿真和随后的整个系统的(局部)启发式优化。提出的研究项目的目标是利用经典优化理论，通过数学上已知的多尺度网络模型对物流进行局部和全局优化，并随后对控制和布局进行优化。最初，单个部件的流动模型是从物理模型推导出来的，因为它们的模拟时间要短得多，而且精度几乎相同。然后，在节点处实现完整物流的网络，从而允许流继续。为了保证物理模型和流动模型的一致性，设计了多尺度网络模型。这种多尺度网络模型是利用网络流模型进行最优全局控制的数学和确定性计算以及利用物理模型进行具体的局部优化的基础。通常，根据目标(基于模拟的优化)手动从各种备选方案中进行最佳选择。然而，这里所描述的最优物流控制的目的是能够通过数学优化策略和数值求解方法来计算最佳方案。在这个研究项目中，将开发算法，首次允许使用确定性的数学方法对物流要素进行全局优化。为了实现里程碑式的建模、多尺度网络模型和最优物流控制，数学和工程科学之间的密切合作是不可或缺的。

Physically based simulation, discrete, event simulation or flow simulation are simulation approaches for improving the material flow of production lines. These methods are generally suitable for simulations of indi-vidual system components and the subsequent (local) heuristic optimization of the entire system. The objec-tive of the proposed research project is the local and global optimization of the material flow by means of the theory of classical optimization by multi-scale network models known from mathematics with a subsequent optimization of control and layout. In the beginning, flow models of individual components are deduced from physics models because their simulation takes much less time with almost the same accuracy. Then a net-work of the complete material flow is implemented at the nodes allowing for the flow to continue. In order to ensure the coherence between the physics model and the flow model, a multi-scale network model is de-signed. This multi-scale network model is the basis for the mathematical and deterministic calculation of the optimal global control by means of the network flow model and a concrete local optimization by means of the physics models. Typically the best selection from the various alternatives is made manually according to the objectives (simulation-based optimization). However, the purpose of the optimal material flow control de-scribed here is to be able to calculate the best alternative by mathematical optimization strategies and nu-merical solution methods. Within this research project algorithms will be developed that for the first time allow the global throughout optimization of material flow elements using deterministic, mathematical methods. For achieving the milestones Modelling, Multiscale Network Models and Optimal Material Flow Control a close cooperation between mathematical and engineering sciences is indispensable.