Optimizing the Hexagonal Fuzzy Transportation Problem With the Novel Dhouib‐Matrix‐TP1 Method

Transportation Problem (TP) is considered a combinatorial optimization problem, and its aim is to minimize the total transportation cost from several sources to different destinations. In this paper, an intensive literature review of the TP is presented in detail with an enhancement of the novel heuristic entitled Dhouib‐Matrix‐TP1 (DM‐TP1) to solve the TP under a hexagonal fuzzy environment. Indeed, all parameters of the TP—such as transportation cost, demand, and supply—are represented using hexagonal fuzzy numbers (HFNs), which offer a richer structure for modeling uncertainty with less information loss compared to triangular or trapezoidal fuzzy numbers. To convert these HFNs to crisp ones, the centroid ranking function is used. After that, the DM‐TP1 method is applied to rapidly find an initial basic feasible solution using the original metric (Average–Min). Experiment results of DM‐TP1 on different literature Hexagonal Fuzzy Transportation Problems (HFTPs) prove its performance. Moreover, DM‐TP1 illustrates graphically the generated solution and allows the decision maker to ergonomically handle the TPs under HFNs.