DISCRETE AND CONTINUOUS Website: www.aimSciences.org DYNAMICAL SYSTEMS Supplement 2009 pp. 790–799 A HYPERBOLIC RELAXATION MODEL FOR PRODUCT FLOW IN COMPLEX PRODUCTION NETWORKS

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 stag