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Ammar, E. E.; Youness, E. A.

Study on multiobjective transportation problem with fuzzy numbers. (English) Zbl 1099.90049

Appl. Math. Comput. 166, No. 2, 241-253 (2005).
Summary: We investigate the efficient solutions and stability of multiobjective transportation problem (FMTP) with fuzzy coefficient \(\widetilde{c}_{ij}^r\in \widetilde{c}^r\) and/or fuzzy supply quantities \(\widetilde{a}_i\) and/or fuzzy demands quantities \(\widetilde{b}_j\). The concept of \(\alpha\)-fuzzy efficient was introduced in which the ordinary efficient solution is extended based on the \(\alpha\)-level of fuzzy numbers. A necessary and sufficient condition for such a solution is established. The basic notions as the solvability set and the stability set of the first kind are defined and characterized. The parametric analysis is used to characterize the parametric optimal solutions to the auxiliary problems. An algorithm for the determination of the stability set is proposed. Finally, a numerical example is given.

Cited in 18 Documents

MSC:

90C27 Combinatorial optimization
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming

Keywords:

Multiobjective transportation problem; Fuzzy numbers; \(\alpha\)-Fuzzy efficient; \(\alpha\)-optimality; Stability notions
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References:

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