Multiscale Continuum Models for Large Production and Supply Networks

生产流是一种强烈的多尺度现象：构建供应链的工厂和配送中心网络代表大流量-长时间尺度网络，而单个机器和操作员网络通常代表局部快速尺度。在描述单独的本地生产单元方面已经取得了很大的进展：离散事件和基于代理的模型被常规地开发来研究通过这样的网络的流动的动力学。然而，由于涉及的过程的随机性和网络的复杂性，这种模拟的维护费用高得令人望而却步，并且没有很好地装备来回答关于网络整体行为的问题。这一提议的目标是为复杂生产网络中的本地和快速时间尺度与全球长期时间尺度之间的联系奠定数学基础。在此基础上，我们将基于产品和生产阶段的连续统近似，推导出网络生产流的连续统仿真模型，从而得到与交通流模型相关的偏微分方程模型。将在连续介质模型和大规模离散事件模拟之间进行比较。作为一个连接小规模模拟和大规模模拟的额外工具，我们还将探索一种对这些生产系统的无方程建模方法。对工厂生产流程的快速和准确模拟有着巨大的需求，在企业层面或整个供应链层面上更是如此，允许用户改变策略和商业场景，并提出假设问题。这是典型的情况，例如在半导体工厂或汽车制造业。目前，由于系统的复杂性、涉及的部件数量和生产的随机性，这些模拟不能作为决策工具的一部分来执行。相反，模拟场景通常是离线完成的，并在计划会议上讨论结果。回答一个新问题通常需要进行详细的离线重新计算。我们的方法有可能通过可扩展的快速模拟来开发描述此类流动的基本模型，并讨论其有效性和局限性。总体而言，我们正在为更好的战略规划和业务评估环境开发理论和工具。

Production flow is a strongly multiscale phenomenon: Networks of factories and distribution centers building a supply chain represent the large flow - long timescale networks, whereas the networks of individual machines and operators typically represent the local fast scales. Much progress has been made to characterize the individual local production unit: Discrete event and agent based models are routinely developed to study the dynamics of flows through such networks. However, due to the stochastic nature of the processes involved and due to the complexity of the networks, such simulations are prohibitively expensive to maintain and are not equipped well to answer questions on the behavior of the networks as a whole. The goal of this proposal is to generate the mathematical foundation for a link between the local and fast time scales and the global long-term time scales in complex production networks. Based on this link we will derive continuum simulation models of network production flows based on continuum approximations for product as well as production stages, leading to partial differential equation models related to traffic flow models. Comparisons between the continuum models and large-scale discrete event simulations will be performed. As an additional tool linking small-scale simulation to large-scale simulation we will also explore an equation-free modeling approach to these production systems.There is a huge need for fast and accurate simulations of production flows in factories and even more so at the enterprise level or at the whole supply chain level allowing the user to vary policies and business scenarios and ask "what if" questions. This is typically true for example in semiconductor factories or car manufacturing. Currently, these simulations suffer from the fact that the complexity of the systems, the number of parts involved and the stochastic nature of production does not allow the simulations to be performed as part of a decision tool. Instead, simulation scenarios are typically done off-line and the results discussed in planning meetings. Answering a new question typically requires a detailed off-line recalculation. Our approach has the potential to develop the fundamental models to describe such flows through a scalable and fast simulation and discuss their validity and limitations. Overall we are developing the theory and the tools for a much better strategy-planning and business-evaluation environment.