A Trapezoidal Membership-Based Multi-Level, Multi-Objective Optimization Model for Solid Transportation Problem under Uncertain Environments

In this study, a comprehensive multiple level, multi-objective solid transportation problem (MOSTP) model is proposed under uncertain environments having trapezoidal values of fuzzy sets. In real-life logistics systems, decision-making involves several hierarchical levels, each with conflicting objectives such as minimizing transportation cost, travel time, and defective items. Conventional models often fail to handle parameter uncertainty caused by fluctuating demand, inconsistent supply, or variable conveyance capacity. The proposed framework converts an uncertain transportation model into a deterministic equivalent using chance-constrained programming, and integrates three alternative compromise approaches: (A) the Weighted Max–Min Approach, (B) the Weighted Sum Approach, and (C) the Max–$\lambda$ Fuzzy Compromise Model. Numerical results validated the consistency and superiority of the fuzzy-based formulation and showed that the Max–$\lambda$ model achieves the highest satisfaction level ($\lambda = 1$) with near-optimal objective values. The approach ensures flexible and robust decisions in complex supply-chain environments.