Optimizing transportation and reducing carbon footprint: a multi-objective approach with carbon cap and offset policy in fixed charge scenarios under type-2 neutrosophic uncertainty

Global warming, driven by urbanization, industrial growth, and increased vehicle usage, has made carbon emission reduction a critical priority for industries alongside their financial goals. This study proposes a multi-objective fixed-charge transportation (MOFCT) model that incorporates type-2 neutrosophic parameters to capture the inherent uncertainty in supply, demand, and other key factors. The model simultaneously optimizes three objectives: total transportation cost, including fixed route cost, preservation cost, and carbon emission costs; transportation time; and product deterioration level. A ranking method is applied to convert the neutrosophic parameters into crisp values for computational analysis. Leontief-scalarized fuzzy programming (LS-FP) is proposed to derive Pareto-optimal solutions, while traditional fuzzy programming (FP) and intuitionistic fuzzy programming (IFP) are used for comparison to assess the relative performance. Numerical experiments demonstrate that fuzzy approaches are more suitable than IFP for generating optimal solutions. The key advantage of neutrosophic sets in this study lies in their ability to represent complex uncertainties more effectively than traditional fuzzy sets, particularly in logistics systems with fluctuating demand. The integration of carbon offset mechanisms ensures that transportation planning aligns with sustainability goals, allowing decision-makers to balance economic objectives with environmental responsibilities. The novelty of this work is in combining type-2 neutrosophic uncertainty with carbon offset policies and product preservation strategies within a multi-objective framework, providing actionable insights for sustainable conscious logistics planning.