Economic damage due to the supply chain turmoil in the past few years has been more severe than the pandemic, labor shortages, and domestic conflict combined. The primary cause of such a crisis is that the current supply chain analysis tool, relying heavily on static optimization, is insensitive to non-eligible changes such as policy changes due to the pandemic. As a result, such analysis needs to be conducted regularly whenever there is a change in the economic environment, which dramatically increases the computational cost. In this paper, the main purpose is to achieve agile sustainability supply chain management through dynamic system modeling and control for production processes of supply chain networks (SCNs), which involves both theoretical and numerical analysis. In particular, we first formulated a chain-like dynamic system to represent the daily production process, which is a discrete-time dynamic system from the control engineering perspective. Then, an optimal control problem can be developed for decision-making on production. Several numerical cases are presented in this paper to demonstrate the applicability of this developed dynamic system and further discuss the potential optimal production.