Modeling and analysis of sustainable supply chain dynamics

This paper studies the dynamic behavior of the interaction between sustainable supply chains and environment. Environmental impact exists at each stage throughout supply chains such as resource extraction, production, distribution, repairs, and waste disposal, among others. As market and competition constantly change over time, however, supply chains interact significantly with environment, so managing supply chains sustainably is dynamic. In this paper, a mathematical model based on nonlinear dynamic system is presented to describe the dynamics of the impact of supply chains on environment while achieving sustainable supply chains. The existence and uniqueness of its solutions are proved, followed by the analysis on its equilibrium and stability. To better understand the dynamic mechanism of this proposed system, performance analysis is conducted with respect to three parameters: (a) design production capacity; (b) environmental cost; and (c) demand rate. Analytical results validate the dynamic interaction of supply chains with environment, and justify the environmental and economic significance of supply chain sustainability.