Profit Maximization in Unbalanced Fuzzy Transportation Networks Using Trapezoidal Fuzzy Modeling and Exact Optimization

Profit-oriented logistics systems operate under considerable uncertainty in profit margins, supply capacities, and demand levels, which challenges traditional transportation modeling assumptions. However, a large portion of the transportation literature still relies on deterministic formulations or simplified fuzzy representations that are not sufficient to reflect parameter stability. Although many fuzzy transportation models have been developed using triangular fuzzy numbers, they are often coupled with heuristic solution methods, which may oversimplify real operational conditions and provide limited insight into the stability of resulting decisions. Consequently, the robustness of such models as practical logistics planning tools remains limited. This paper proposes a solver-based optimization model for profit maximization in unbalanced transportation networks under uncertainty. Trapezoidal fuzzy numbers are used to represent imprecise profits, supplies, and demands, explicitly capturing stable operational ranges under both optimistic and pessimistic scenarios. A structured defuzzification approach is employed to compute decision-ready parameters, while the resulting linear programming model guarantees globally optimal solutions. The proposed framework is demonstrated through an applied case study based on the Egyptian petroleum distribution network. The results show that the model produces consistent profit outcomes and stable shipment decisions across different uncertainty levels and defuzzification rules. Furthermore, sensitivity and robustness analyses confirm that the dominant allocation patterns remain stable under moderate variations in the uncertainty structure, supporting the practical relevance of the proposed approach as an effective decision-support tool for transportation planning.