Abstract
This paper presents an algorithm to solve a fuzzy transportation problem in which demand, supply and transportation costs are uncertain. Existing solution methods convert a fuzzy transportation problem into two or more crisp transportation problems and solves it. But, the proposed algorithm solves a fuzzy transportation problem without converting it into a crisp transportation problem. This approach results in a fuzzy total transportation cost, which is a fuzzy number. Sudhagar score method is used to rank fuzzy numbers. In comparing results of existing methods with the proposed method, this algorithm outperforms the previous ones. Two numerical examples explain working procedure of the proposed algorithm.
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Notes
Equality is defined according to (iv) of Remark 1.
Allocations of a transportation problem are said to be in independent positions if it is not possible to alter any individual allocation without either rearranging the positions of the allocations or violating the supply and demand constraints.
An independent cell is one from which a closed path cannot be traced.
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Chandran, S., Kandaswamy, G. A fuzzy approach to transport optimization problem. Optim Eng 17, 965–980 (2016). https://doi.org/10.1007/s11081-012-9202-6
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DOI: https://doi.org/10.1007/s11081-012-9202-6