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Logistics companies are facing increasing pressure to implement sustainable practices as environmental issues across the world worsen. Through a thorough performance-based assessment of green supply chains, this research investigates how sustainability might be included into logistical operations. Eight important indicators were chosen using an evaluation framework to evaluate the operational and environmental performance of logistics companies. These indicators ranged from energy efficiency and carbon emissions reduction to green procurement and digital monitoring. As alternatives, ten typical logistics models and methods were chosen, each of which reflected a different level of sustainability integration. To evaluate and rank these models according to their green performance, the study uses both qualitative and quantitative data along with formal decision-making procedures. This study uses the Multipolar Interval-Valued Neutrosophic Soft Set to overcome uncertainty. Results show that investments in renewable energy, digital innovation, and circular logistics techniques greatly improve sustainability results. The study provides practical insights for industry stakeholders and policymakers dedicated to sustainable supply chain transformation, emphasizing the crucial role that strategic decision-making and policy alignment play in advancing eco-efficient logistics systems.