A continuum model for a re-entrant factory

A continuum model for a re-entrant factory

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Article ID: iaor20081203
Country: United States
Volume: 54
Issue: 5
Start Page Number: 933
End Page Number: 950
Publication Date: Sep 2006
Journal: Operations Research
Authors: , , , ,
Abstract:

High-volume, multistage continuous production flow through a re-entrant factory is modeled through a conservation law for a continuous-density variable on a continuous-production line augmented by a state equation for the speed of the production along the production line. The resulting nonlinear, non local hyperbolic conservation law allows fast and accurate simulations. Little's law is built into the model. It is argued that the state equation for a re-entrant factory should be nonlinear. Comparisons of simulations of the partial differential equation model and discrete-event simulations are presented. A general analysis of the model shows that for any nonlinear state equation there exist two steady states of production below a critical start rate: A high-volume, high-throughput time state and a low-volume, low-throughput time state. The stability of the low-volume state is proved. Output is controlled by adjusting the start rate to a changed demand rate. Two linear factories and a re-entrant factory, each one modeled by a hyperbolic conservation law, are linked to provide proof of concept for efficient supply chain simulations. Instantaneous density and flux through the supply chain as well as work in progress and output as a function of time are presented. Extensions to include multiple product flows and preference rules for products and dispatch rules for re-entrant choices are discussed.

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