Stability Limits of Coordinated Supply Chains Under Transportation Delays: Implications for Resilient Logistics Design

Recent global disruptions have exposed the fragility of tightly coordinated supply chains, particularly under transportation and information delays, motivating the need for analytical tools to assess their stability limits. This study analyzes a two-echelon supply chain system to determine how delays affect stability and performance, with an emphasis on the role of feedback coordination. A continuous-time delay-differential modeling framework was developed to examine both uncoupled and coupled configurations. Stability is analyzed through characteristic equations, and explicit closed-form expressions for the critical delay threshold are derived as functions of the coupling gain and shipment rate. The uncoupled system is shown to exhibit delay-independent marginal stability but lacks the ability to regulate downstream inventory. In contrast, the coupled system achieves inventory regulation but introduces delay-dependent stability with a critical delay, beyond which oscillations grow unbounded. A key result revealed an inverse relationship between coupling strength and delay tolerance, highlighting a trade-off between responsiveness and robustness. An optimal control formulation further demonstrates that the stability constraints limit the achievable performance. These findings provide a theoretical explanation for the vulnerability of just-in-time systems and offer practical guidelines for resilient logistics design, enabling supply chain practitioners to quantify stability margins and balance coordination efficiency with robustness to transportation delays.