Abstract
Modern requirements necessitate the establishment of sustainable transportation systems, considering the substantial growth in transportation activities over recent years, which is expected to continue. Companies are facing the challenge of modeling their system transport to align with green principles. Sustainable transport relied on involving diverse stakeholders, particularly scientific research, in the development of this field. In light of this, maintaining sustainable transport quality involves conducting thorough investigations into an innovative study focusing on an uncertain interval programming model for a multi-stage, multi-objective, multi-product transportation challenge within budget constraints and safety measures in a green supply chain. Human languages often contain imperfect or unknown information, inherently lacking certainty; achieving precision in describing existing states or future outcomes is frequently unattainable. In probability theory, sufficient historical information is crucial for estimating probability distributions; while in fuzzy theory, determining a reliable membership function proves challenging; hence, there is often a hesitant estimation of the degree of belief in the occurrence of each condition. Addressing such uncertainties, the theory of uncertain intervals proves highly valuable. Given these considerations, the elements of the specified problem are recognized as uncertain intervals. To manage this lack of assurance, a fusion of interval theory and methods from uncertain programming is used to formulate two distinct models: an expected value model and a chance-constrained model. The equivalent deterministic models are then formulated and solved utilizing Weighted Sum Method, fuzzy programming, and goal programming. Following this, a numerical example is utilized to assess the model’s performance, and the results obtained are compared. Finally, the document concludes with a sensitivity analysis and outlines future directions.