Affiliations: Industrial Engineering Faculty, Islamic Azad University, South Tehran branch, Tehran, Iran
Correspondence:
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Corresponding author. Amir Abbas Shojaie, Industrial Engineering Faculty, Islamic Azad University, South Tehran branch, Tehran, Iran. E-mail: amir@ashojaie.com.
Abstract: Nowadays, one of the most challenging issues for firms, organizations and factories is transportation problems. Major of annual costs is related to these problems. Besides, according to the importance of environmental issues and strict laws for protecting the environment, organizations and firms ought to find the most economical and cleaner ways of transportation. In this paper, we optimized a two-objective fuzzy transportation problem simulated by multi-objective linear integer fuzzy programming technique. The existing fuzzy parameters (transportation costs, demands and supply quantities) are considered triangular fuzzy numbers. The Jimenez method used for Defuzzification the fuzzy model. In addition to principal constraints of transportation problems, the constraints of real-world such as vehicles’ capacity and most shipping time are also included. In order to solve the fuzzy transportation problem, simulated annealing (SA) approach and non-dominated sorting genetic algorithm (NSGA-II) (which has rarely been used) implemented. The results of solving some test problems created in different sizes show that both methods are capable of finding Pareto solutions in a quick time. The results of the comparison between the named algorithms prove that the SA algorithm comes up with more Pareto solutions with better quality in a shorter time than NSGA-II.
Keywords: Green transportation problem, multi-objective linear integer mathematical programming, simulated annealing (SA), non-dominated sorting genetic algorithm (NSGA-II), Jimenez method
