Multi-objective closed-loop supply chain inventory model with learning and forgetting under carbon emission policies using NSGA-II, MOPSO, and TOPSIS

This study investigates the impact of workers’ good practices in remanufacturing, manufacturing, and inspection processes under the learning and forgetting (LaF) framework on total cost and carbon emissions in a closed-loop supply chain (CLSC) inventory model. The investigation is conducted under three carbon emission reduction policies: carbon tax (CT), cap-and-offset (CCO), and cap-and-trade (CCT). Workers’ involvement in the continuous learn-forget-learn process across different tasks in the CLSC, including remanufacturing, manufacturing, machine operation, inspection, and correcting production errors, boosts productivity and process quality. The main focus for the CLSC participants is sustainability, emphasizing the improvement of worker experience to enhance productivity and process quality, aiming to minimize total cost and carbon emissions. First, the multi-objective optimization problems are formulated under the CT, CCO, and CCT policies while incorporating LaF effects. The total cost function serves as the first objective, while the carbon emission function constitutes the second. The non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are employed to solve the optimization model, with their parameters fine-tuned using Taguchi analysis. Pareto fronts are generated to identify optimal solutions, and the best solutions are selected using multi-criteria decision analysis (MCDA) with the technique for order preference by similarity to an ideal solution (TOPSIS). A statistical analysis is conducted to compare the performance of NSGA-II and MOPSO. Numerical results reveal that learning significantly reduces total costs and carbon emissions across all three policies. A comparative analysis of the policies with and without the LaF effect indicates that the CCT policy with LaF is the most effective in reducing total costs and emissions in the CLSC. Sensitivity analysis further highlights the impact of parameter variations on total costs and carbon emissions under different policies. As the learning exponent (LE) increases from 0 to 0.415, total costs and carbon emissions steadily decline. Under the CT policy, average costs decrease by 2.65%, while carbon emissions are reduced by 4.76%. The CCO policy results in reductions of 2.58% in costs and 5.86% in emissions. In contrast, the CCT policy exhibits the most significant improvements, with cost reductions of 3.84% and emission reductions of 6.93%.