A continuum model for a re-entrant factory

Title
A continuum model for a re-entrant factory
Authors
Armbruster, D.; Marthaler, D.E.; Ringhofer, C.; Kempf, K.; Jo, T.C.
Keywords
SUPPLY CHAINS, FLUID MODELS
Issue Date
2006-09
Publisher
INST OPERATIONS RESEARCH MANAGEMENT SCIENCES
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, nonlocal 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 (PDE) 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 (WIP) 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.
URI
http://dspace.inha.ac.kr/handle/10505/1966
ISSN
0030-364X
Appears in Collections:
College of Natural Science(자연과학대학) > Mathematics (수학) > Journal Papers, Reports(수학 논문, 보고서)
Files in This Item:
A comtinuum.pdfDownload

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