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.
