Modeling Uncertainty in Logistics: Optimizing Fuzzy Transportation under Interval-Valued Trapezoidal Fuzzy Numbers

Abstract

This study addresses the transportation problem under imprecise conditions by employing Interval-Valued Trapezoidal Fuzzy Numbers (IVTrFNs) to model uncertain parameters including transportation costs, supplies, and demands. The primary contribution of this research is the development of a novel optimization framework based on a weighted linear ranking function, complemented by a thorough theoretical analysis of its properties. This function effectively transforms IVTrFN parameters into crisp values through a parameter z, which allows the decision-maker to incorporate their strategic outlook by weighting the lower and upper bounds of the fuzzy intervals. The proposed method significantly streamlines the solution process, reducing the computational burden commonly associated with complex fuzzy arithmetic operations. The efficacy of the approach is validated through a comprehensive numerical example involving two supply sources and three demand destinations. The computational results reveal a compelling insight: as the parameter z increases from 0 to 1, reflecting a transition from a pessimistic to an optimistic outlook, the total transportation cost decreases by approximately 2.59 times. This finding carries substantial implications for logistics management, demonstrating that strategic orientation toward uncertainty can dramatically influence operational costs. The proposed framework equips managers with a practical, theoretically-grounded decision-support tool for designing optimal transportation strategies under uncertainty.