  Despite recent developments in management theory, maintaining a manufacturing
schedule remains difficult because of production delays and fluctuations in
demand and supply of materials. The response of manufacturing systems to such
disruptions to dynamic behavior has been rarely studied. To capture these
responses, we investigate a process that models the assembly of parts into end
products. The complete assembly process is represented by a directed tree,
where the smallest parts are injected at leaves and the end products are
removed at the root. A discrete assembly process, represented by a node on the
network, integrates parts, which are then sent to the next downstream node as a
single part. The model exhibits some intriguing phenomena, including overstock
cascade, phase transition in terms of demand and supply fluctuations,
nonmonotonic distribution of stockout in the network, and the formation of a
stockout path and stockout chains. Surprisingly, these rich phenomena result
from only the nature of distributed assembly processes. From a physical
perspective, these phenomena provide insight into delay dynamics and inventory
distributions in large-scale manufacturing systems.
