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Abstract. Supply chains are essential for minimizing costs, improving customer satisfaction, and increasing profitability. This paper introduces an innovative perspective on supply chains as a control problem, presenting a distinctive approach for addressing this issue. Mathematical modeling of the supply chain is conducted, considering system dynamics and employing optimal control techniques. This mathematical model is represented through a set of ordinary differential equations applied to both dynamic open-loop and closed-loop supply chains, with an emphasis on environmental sustainability (reducing waste and carbon emissions) and flexibility in managing demand disruptions and supply crises. We analyze production rates and capacities at each node within the supply chain network, emphasizing the balance between the inflow and outflow of raw materials. Additionally, sensitivity and stability analyses for open-loop and closed-loop supply chains are performed to gain insights into how various parameters influence system performance. To enhance supply chain efficiency, we propose an energy-based optimal control strategy structured across six layers for the closed-loop supply chain. A comprehensive evaluation of the proposed method assesses its effectiveness in significantly reducing waste, enhancing resilience against disruptions, and achieving economic and environmental objectives. The findings indicate that our proposed approach can effectively enhance supply chain performance, facilitating the achievement of both economic and environmental objectives.
Keywords: Dynamic Open-Loop Supply Chain, Dynamic Closed-Loop Supply Chain, Inventory Level, Optimal Control, Stability, Environmental Sustainability, Flexibility.
Type of Article: Research paper |
Subject:
Special
Received: 2024/09/6 | Accepted: 2025/07/7 | ePublished ahead of print: 2025/11/24
Received: 2024/09/6 | Accepted: 2025/07/7 | ePublished ahead of print: 2025/11/24
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