Summary: A continuous model for supply chains with finite buffers
September 21, 2010
An aggregate continuum model for production flows and supply chains with finite
buffers is proposed and analyzed. The model extends earlier partial differential equations
that represent deterministic coarse grained models of stochastic production systems based
on mass conservation. The finite size buffers lead to a discontinuous clearing function
describing the throughput as a function of the work in progress. Following previous work
on stationary distribution of WIP along the production line, the clearing function becomes
dependent on the production stage and decays linearly as a function of the distance from
the end of the production line. A transient experiment representing the break down of the
last machine in the production line and its subsequent repair is analyzed analytically and
numerically. Shock waves and rarefaction waves generated by blocking and re-opening of
the production line are determined. It is shown that the time to shutdown of the complete
flow line is much shorter than the time to recovery from a shutdown. The former evolves
on a transportation time scale whereas the latter evolves on a much longer time scale.
Comparisons with discrete event simulations of the same experiment are made.