 
Summary: MULTISCALE MODEL. SIMUL. c 200X Society for Industrial and Applied Mathematics
Vol. 0, No. 0, pp. 000000
THERMALIZED KINETIC AND FLUID MODELS FOR
REENTRANT SUPPLY CHAINS
D. ARMBRUSTER AND C. RINGHOFER
Abstract. Standard stochastic models for supply chains predict the throughput time (TPT) of
a part from a statistical distribution, which is dependent on the work in progress at the time the
part enters the system. So they try to predict a transient response from data which are sampled
in a quasisteadystate situation. For reentrant supply chains this prediction is based on insufficient
information, since subsequent arrivals can dramatically change the TPT. This paper extends these
standard models by introducing the concept of a stochastic phase velocity which dynamically updates
the TPT estimate. This leads to the concepts of temperature and diffusion in the corresponding
kinetic and fluid models for supply chains.
Key words. reentrant supply chains, traffic flow models, Boltzmann equation, Chapman
Enskog, fluid limits
AMS subject classifications. 65N35, 65N05
DOI. 10.1137/030601636
1. Introduction. This paper is concerned with models for supply chains with
reentrant nodes and their macroscopic, i.e., long term, limits, resulting in a modifi
cation of standard discrete event simulation algorithms. Generally, a supply chain is
