Optimizing green solid transportation with carbon cap and trade: a multi-objective two-stage approach in a type-2 Pythagorean fuzzy context

Recently, it has been observed that the weather is changing constantly because of global warming. The government is urging everyone, including scientists and the general public, to help address the severe challenges caused by climate change. Addressing the pivotal issue of carbon emissions stemming from transportation, this manuscript delves into the development of an efficient and coordinated management system. The proposed solution involves a green solid transportation system employing a two-stage network to implement a carbon cap and trade policy. A mathematical model is introduced to underscore the significance of this approach. Because of market fluctuations, supply and demand constraints are not always the same. Therefore, a two-folded uncertainty is included in this article for a better realistic outcome. A ranking defuzzification approach is employed to convert this uncertainty into a deterministic measure. Two illustrative numerical case studies are presented to underscore the effectiveness and feasibility of the proposed approaches. Then, three multi-objective techniques are employed to obtain Pareto-optimal solutions for the addressed problem. After that, a comparative study among these techniques is introduced and a sensitivity analysis is added to explore how the objective functions are influenced by potential changes in supply and demand. In conclusion, the paper offers important insights and identifies areas for future research in this field.