Complexity analysis of output and recycling rate decisions of cross-border supply chain system under four recycling modes

Abstract To investigate the impact of recycling modes on the stability of cross-border supply chain (SC) systems, this paper decomposes a cross-border SC system, consisting of two countries with different recycling capabilities for electronic products, such as Singapore and Vietnam, into three product-market chains (PMCs). Discrete dynamical models for output and recycling rate decisions of the system are developed based on four recycling modes. The Nash equilibrium solutions and stability conditions of the models are obtained via nonlinear dynamics principles; the stable regions and chaotic phenomena of the system, and the impact of tariff on the system stability are investigated through numerical simulation. Our findings suggest that to ensure the system stability, PMCs should adjust output and recycling rates, respectively, at low speeds. Retailer recycling mode shows the largest stable region of system decisions. When the adjustment speeds of output and recycling rate increase, the stable regions of the system in the four recycling modes are compacted. In addition, an increase in tariff levels can adversely affect the system stability. Finally, increasing recycling prices and marginal recycling transaction costs can expand the stable regions of the system, mitigate the adverse impact of tariffs, and enhance the profit stability of the closed-loop PMC.