This study aims to explore the Grey Fuzzy Transportation Problem, which describes the decision-making processes under uncertainty in the transportation problem, which is an especially important study problem for the logistics sector and academic studies. Comprehensive analyses and suggestions are made to contribute to the effective solution of the Grey Fuzzy Transportation Problem and better control of transportation problems which contain uncertainty. In the research, four different optimization methods for the Grey Fuzzy Transportation Problem (GFTP), the Closed Path Method, Interval Optimization, Robust Optimization and Interval Optimization with Penalty Function, are comparatively analyzed. The analyses are done on a total of 40 test problems with four different problem sizes, small, medium, large and extra-large. The results revealed that Interval Optimization and Robust Optimization performed the best in terms of solution quality and computation time. In particular, extensive analyses on the Interval Optimization with Penalty Function method verified that this is an effective and consistent solution approach for GFTP.