Solving a fuzzy fixed charge solid transportation problem by metaheuristics

This paper investigates a fixed charge solid transportation problem (FCSTP) under a fuzzy environment, in which the both direct and fixed costs are supposed to be fuzzy numbers. This is one of the primary and most important problems in transportation and network research areas. To solve such a hard problem, three metaheuristics, namely variable neighborhood search (VNS), simulated annealing (SA) and hybrid VNS are employed. To the best of our knowledge, neither SA nor VNS has been considered for any kind of transportation problems. Besides, the novelty of the proposed algorithms is to use various new neighborhood structures related to the nature of the problem, which are proposed and used for the first time. The efficiency of employed parameters is measured by the Taguchi experimental design method that is a useful and new approach to tune the parameters and reduce the possible number of experiments in this research area. To evaluate the performance of the proposed algorithms, an extensive computational study has been conducted and the associated results obtained by the algorithms are compared with each other. Finally, a conclusion and further research areas are presented.