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DISCRETE AND CONTINUOUS Website: www.aimSciences.org DYNAMICAL SYSTEMS
 

Summary: DISCRETE AND CONTINUOUS Website: www.aimSciences.org
DYNAMICAL SYSTEMS
Supplement 2009 pp. 790799
A HYPERBOLIC RELAXATION MODEL FOR PRODUCT FLOW
IN COMPLEX PRODUCTION NETWORKS
Ali Unver, Christian Ringhofer and Dieter Armbruster
Department of Mathematics and Statistics
Arizona State University, Tempe, AZ 85287-1804, USA
Abstract. This paper presents a continuum - traffic flow like - model for the
flow of products through complex production networks, based on statistical
information obtained from extensive observations of the system. The resulting
model consists of a system of hyperbolic conservation laws, which, in a relax-
ation limit, exhibit the correct diffusive properties given by the variance of the
observed data.
1. Introduction. We present a continuum - traffic flow like - model for the evo-
lution of a large number of parts through a complex production system. The basic
idea of traffic flow like models for production systems is to model the evolution of
parts as moving on a virtual 'road', introducing an artificial spatial variable, namely
the stage of the production process. So, the raw part enters the system at stage
x = 0 and the finished part leaves the system at stage x = 1. In the work presented

  

Source: Armbruster, Dieter - Department of Mathematics and Statistics, Arizona State University

 

Collections: Mathematics