Integrated Sustainable Inventory and Remanufacturing Optimization in a Circular Economy: A Two-Echelon Supply Chain Approach Under Carbon Regulations

 Production systems prioritize economic efficiency, often overlooking environmental sustainability. Growing environmental awareness has led to circular production systems that integrate economic and ecological goals. This study presents a sustainable production–inventory model for a two-echelon supply chain with a manufacturer and retailer, incorporating remanufacturing under carbon emissions regulations. The manufacturing process follows a price and time-dependent demand while remanufacturing relies on a circularity index demand. Two model variants are analyzed using Hessian algorithms, combining cap-and-trade and carbon tax policies with different demand rates and profit functions. Results show that maximum profit occurs under cap-and-trade, despite an 82.20% circularity index. Carbon regulations effectively reduce emissions but slightly lower profitability. This study highlights the need to optimize inventory and remanufacturing decisions to balance economic and environmental goals within a circular economy.