MATHEMATICAL MODELING AND OPTIMIZATION OF CIRCULAR ECONOMY PROCESSES

Abstract

The transition from linear production and consumption systems to circular economy processes requires rigorous quantitative tools to support sustainable decision-making. This study proposes a unified mathematical modeling and multi-objective optimization framework to improve economic performance, environmental impact, and material circularity in circular economy systems. The model explicitly represents forward and reverse material flows and incorporates recovery, capacity, and environmental constraints within an integrated optimization structure. A multi-objective solution strategy is applied to balance total operational cost, emissions, and recovery levels. The applicability of the framework is demonstrated through a numerical case study inspired by waste management and material recovery systems. Results indicate that the optimized circular configuration achieves a recovery level of 68 % of total demand, leading to a reduction of carbon emissions from 30,600 kilograms to 21,360 kilograms, while total system cost increases from 232,000 United States dollars to 248,400 United States dollars. Compared to a linear baseline scenario, disposal volumes are reduced by 68 %, highlighting the effectiveness of recovery-oriented decision-making. The findings confirm that integrating circularity as a primary optimization objective enables decision-makers to identify balanced solutions that support long-term sustainability goals while maintaining economic feasibility. The proposed framework offers a generalizable and scalable approach that can be adapted to diverse circular economy applications, providing valuable insights for managers and policymakers seeking to operationalize circular economy strategies.