A Continuum Model for a Re-entrant Factory

Dieter Armbruster (), Daniel E. Marthaler (), Christian Ringhofer (), Karl Kempf () and Tae-Chang Jo ()
Additional contact information
Dieter Armbruster: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804
Daniel E. Marthaler: Northrup Grumman Integrated Systems, Western Region, 17066 Goldentop Road, 9V21/R3-2, San Diego, California 92127-2412
Christian Ringhofer: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804
Karl Kempf: Decision Technologies, Intel Corporation, 5000 West Chandler Boulevard, MS CH3-10, Chandler, Arizona 85226
Tae-Chang Jo: Mathematics Department, Inha University, 253, Yonghyun-Dong, Nam-Ku, Incheon, 402-751, South Korea

Operations Research, 2006, vol. 54, issue 5, 933-950

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.

Keywords: production/scheduling: approximations; simulations: efficiency; mathematics (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.1060.0321 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:54:y:2006:i:5:p:933-950

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().