Project Title: Multiscale Continuum Models for Large Production and Supply Networks
PIs: Christian Ringhofer , Dieter Armbruster
Sponsor: NSF, 2006-2010

Awardee: Arizona State University
Award Number: 0604986

Students: N. Brewer, M. Cameron, M. Lamarca, A. Unver,

The modelling of production flow is inherently multiscale problem:Networks of factories and distribution centers, building a supply chain, represent the long - timescale regime, whereas individual machines and operators typically represent the local fast scales. Much progress has been made in characterizing 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 timescales and the global long term timescales 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.\\

{\bf Intellectual merit:}

This proposal bridges many-particle physics, stochastic simulations and engineering of production flows: To derive macroscopic transport equations from the microscopic stochastic behavior of a large number of individual units we follow the old program of Boltzmann and Maxwell, deriving gas transport equations from kinetic theory. The challenge here is that the flow, while partially governed by 'factory -physics' is not entirely determined by it.

The physical constraints that are hard or impossible to change are mass conservation, capacity limits of production units, or the flow topologies of production. Human or economical constraints however also have a decisive influence on the behavior of the flow: Dispatch policies decide which step or product in a production line is favored, economic constraints determine the production capacity and human behavior influences the stochastic nature of the production process. Hence, in addition to the kinetic theory, there will always be heuristic elements in these models in addition to the approximations by going to the continuum. A second focus of the proposal therefore lies in the macroscopic characterization of the nodes (factories) inside a supply chain network. This is done via benchmarking, parameterization and validation of the theoretically developed models. We specifically will work on the re-entrant production flows typical in semiconductor manufacturing.

These comparisons will therefore be done between the continuum models on one hand and large scale discrete event simulations of semiconductor production flows and with reality in factory production at INTEL on the other hand. 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.\\

{\bf Impact:}\

The impact of this project is potentially very high: 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 in real time. Not only large companies like INTEL are interested in these simulations, any entity that deals with large scale flows, be that information flows or a product flows, typically simulates their flows before they actually run full scale experiments. In that sense military supply lines and the flow of information through the internet potentially are impacted by this research: All high volume flows of individual units/parts that flow through many stages of a network that today are simulated at the scale of parts and stages suffer from the fact that the complexity of the systems and the number of parts do not allow the simulation to scale up. As a result, simulations of, for instance, factory production is typically done off line and the results entered as parameters into the overall supply chain planning. Any change in the parameter 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.