An eco-friendly closed-loop supply chain facing demand and carbon price uncertainty

The greenhouse gas emissions due to the energy use in production and distribution in a supply chain are of interest to industries aiming to achieve decarbonization. The industry subjected to carbon regulations require recycling and reusing materials to promote a circular economy through a closed-loop supply chain (CLSC). In this research, we propose a two-stage stochastic model to design the CLSC under a carbon trading scheme in the multi-period planning context by considering the uncertain demands and carbon prices. We also provide a four-step solution procedure with scenario reduction that enables the proposed model to be solved using popular commercial solvers efficiently. This solution makes the proposed model distinguished from the existing models that assume the firms can purchase or sell carbon credits without quantity limitation. The application of the proposed model is demonstrated via simulation-based analysis of the aluminum industry. The results that the proposed stochastic model generates a network with capacity redundancy to cope with the varying customer demands and carbon prices, while only a slight increase in cost and emission is observed compared with the deterministic model. Furthermore, using scenario reduction, the model solved with 80% of the scenarios share the same CLSC network configuration with the model with full scenarios, while the deviation of the total costs is less than 0.53% and the computational burden can be diminished by more than 40%. This research is expected to be useful to solve optimization problems facing large-scale scenarios with known occurrence probabilities aiming for energy conservation and emissions reduction.