On Stability Analysis and Parametric Design of Supply Networks Under the Presence of Transportation Delays

Abstract

Management of interconnected manufacturing units, supply networks, constitutes a timely, but challenging problem in Physics, Operations Research and Mathematics, as it carries very rich dynamics. At the first stage, a very well understanding of the underlying mechanisms and interactions within the hierarchical construct of such networks is required. For this pursuit, a more realistic approach is proposed in this paper, which takes into account the presence of naturally existing transportation delays of supplies in between individual production units. In general, the presence of delays in the dynamics imports another source of instability, which needs to be addressed. However, it is well-known that a thorough stability analysis against delays carries complications, thus it is non-trivial. We present analytical techniques to tackle such difficulties, surfacing allowable transportation delays within the supply network that guarantees stable stock levels. This, in parallel, enables the selection of production rates assuring the supply network to operate in a stable regime. Moreover, we show that under certain parametric settings, the supply network dynamics may become highly sensitive against the presence of delays, which in turn, initiates an undesirable phenomenon called bullwhip effect. We present case studies demonstrating the bullwhip effect and suggesting parametric selections to avoid this undesired behavior within supply networks.