A direct solution approach based on constrained fuzzy arithmetic and metaheuristic for fuzzy transportation problems

This paper presents a novel direct solution approach for fully fuzzy transportation problems in which all of the model parameters as well as decision variables are considered as fuzzy numbers. In detail, a fuzzy decoding procedure based on constrained fuzzy arithmetic operations and a fuzzy ranking technique is first introduced for solution of the problem directly without any fuzzy to crisp transformation process. Then, this decoding procedure is embedded into a metaheuristic, namely priority-based PSO algorithm for generating new solution vectors and seeking for better fuzzy acceptable solutions. By making use of the constrained fuzzy arithmetic concept, the proposed approach is also able to handle the decision maker's attitude toward risk. In order to show validity and applicability of the proposed approach, numerical examples on both balanced and unbalanced fully fuzzy transportation cases are generated and solved. The computational results have shown that relatively more precise and information efficient solutions can be obtained from the proposed approach for risk-averse and partially risk-averse decision makers. Furthermore, the proposed approach is also able to produce fuzzy solutions for risk seekers with high degree of uncertainty similar to the other methods available in the literature.