On Stability Problems of Supply Networks Constrained With Transport Delay

Transportation is one of the most crucial components in supply networks. In transportation lines, there exists a finite time between products leaving a point and arriving to another point in the supply network. This period of time is the delay, which accompanies all transportation lines present in the entire network. Delay is a well-known limitation, which is inevitable and pervasive in the network causing synchronization problems, fluctuating or excessive inventories, and lack of robustness of inventories against cyclic perturbations. The end results of such undesirable effects directly reflect to costs. This paper is motivated to reveal the mechanisms leading to these problems by analytically characterizing qualitative behavior of supply network dynamics modeled by continuous-time differential equations. The presence of delay forms the main challenge in the analysis and this is tackled by developing/utilizing the tools emerging from delay systems and control theory. While the backbone of the paper addresses the qualitative behavior in presence of a single delay representing delays in all transportation paths, it also reveals how to choose production rates and transportation delay without inducing any undesirable effects mentioned. Thorough cases studies with single and multiple delays are presented to demonstrate the effectiveness of the approaches proposed.