An Optimization Approach to the Transportation Problem Using Triangular Fuzzy Numbers

Uncertainty in transportation costs, supply, and demand is a common challenge in real-world logistics systems, making classical transportation models with precise data assumptions inadequate. To address this issue, this paper presents an optimization approach to the transportation problem using Triangular Fuzzy Numbers (TFNs) along with a new defuzzification technique. The fuzzy transportation costs are expressed through optimistic, most likely, and pessimistic values to better represent real operating conditions. The proposed defuzzification method transforms the fuzzy model into a crisp equivalent while preserving uncertainty information more effectively than existing defuzzification approaches such as centroid and graded mean methods. The resulting crisp transportation problem is solved using standard procedures, including an initial basic feasible solution and optimization via the MODI method. Numerical examples and comparative results demonstrate that the proposed approach provides more stable, realistic, and reliable solutions than traditional methods, thereby offering improved decision-making support for transportation and supply chain systems under uncertainty.