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An alternate method for finding more for less solution to fuzzy transportation problem with mixed constraints

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Abstract

In this paper, we present a different process for the optimal solution to mixed constraints transportation problem with imprecise coefficients without changing to its crisp equivalent form which is very distinct from other existing methods. Here, all the variables are considered to be triangular fuzzy numbers. Utilizing a parametric form of triangular fuzzy numbers such as left fuzziness index, right fuzziness index, modal value and by using proposed algorithm, we obtained the initial basic fuzzy feasible solution to the problem without changing to its crisp equivalent form. To obtain the solution, we use fuzzy ranking dependent on left and right spreads at some S-level of fuzzy numbers and fuzzy arithmetic dependent on both location index function and fuzziness index function. We further discuss the more for less solution by obtaining shadow prices to the problem. The more for less situation occurs when we raise the supplies, and demand quantities may cause to reduce the optimal transportation cost. The more for less paradox is very useful to a manager in dynamic, for example expanding an item house loading level or plant age breaking point and publicizing attempts to build request at explicit markets. A numerical example is solved to show the adequacy of the proposed algorithm.

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Authors and Affiliations

Authors

Contributions

All the three authors were mutually worked together to propose a new technique and convert into a manuscript format for finding optimal solution in fuzzy transportation problem.

Corresponding author

Correspondence to P. Uma Maheswari.

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The authors declare that they have no conflict of interest.

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The proposed technique is a new technique, and it is not published in any other journal.

Additional information

Communicated by Vicente Garcia Diaz.

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Vidhya, V., Uma Maheswari, P. & Ganesan, K. An alternate method for finding more for less solution to fuzzy transportation problem with mixed constraints. Soft Comput 25, 11989–11996 (2021). https://doi.org/10.1007/s00500-021-05664-x

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