Unbalanced fully fuzzy solid transportation problem: Solution strategy and some novel prospects

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This study investigates the unbalanced solid transportation problem in a fuzzy environment by looking at the importance of solid transportation problem over classical transportation where the supply of sources and the capacity of vehicles are less than the demand for destinations. The solution of such problems obtained by the existing methods involves a dummy source/dummy vehicle or both, but in reality the dummy source or dummy vehicle has no physical significance and the quantity transported either by the dummy source or by the dummy vehicle is not actually transported. In these situations, the demand for some of the destinations remains unfulfilled and the problem is still unsolved in terms of real-life applications. So, the main question is to find the availability of which of the existing sources and the capacity of which vehicle should be increased to fulfill the total destination requirements with the minimum transportation cost possible. To our knowledge, no existing method in the literature could provide us this information. Therefore, a new method has been proposed to fill this gap. By analyzing the optimal solution obtained through the proposed method, we can identify the availability of which sources and the capacity of which vehicles should be increased to fully satisfy demand. Due to the uncertainty occurring in evaluating the parameters of the real-life problem, the data have been considered as triangular fuzzy numbers, and a fuzzy optimal solution is obtained for the same. Finally, a real-life unbalanced solid transport problem is solved to demonstrate the applicability of the suggested methodology.