Abstract
To the best of our knowledge, till now there is no method described in literature to find exact fuzzy optimal solution of balanced as well as unbalanced fully fuzzy multi-objective transportation problems. In this paper, a new method named as Mehar’s method, is proposed to find the exact fuzzy optimal solution of fully fuzzy multi-objective transportation problems (FFMOTP). The advantages of the Mehar’s method over existing methods are also discussed. To show the advantages of the proposed method over existing methods, some FFMOTP, which cannot be solved by using any of the existing methods, are solved by using the proposed method and the results obtained are discussed. To illustrate the applicability of the Mehar’s method, a real life problem is solved.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Ammar E.E., Youness E.A.: Study on multiobjective transportation problem with fuzzy numbers. Appl. Math. Comput. 166, 241–253 (2005)
Aneja Y.P., Nair K.P.K.: Bicriteria transportation problem. Manag. Sci. 25, 73–78 (1979)
Bellman R.E., Zadeh L.A.: Decision making in a fuzzy environment. Manag. Sci. 17, 141–164 (1970)
Das S.K., Goswami A., Alam S.S.: Multiobjective transportation problem with interval cost, source and destination parameters. Eur. J. Oper. Res. 117, 100–112 (1999)
Diaz J.A.: Solving multiobjective transportation problems. Ekonomicky-matematicky Obzor 14, 267–274 (1978)
Diaz J.A.: Finding a complete description of all efficient solutions to a multiobjective transportation problem. Ekonomicky-matematicky Obzor 15, 62–73 (1979)
Gupta P., Mehlawat M.K.: An algorithm for a fuzzy transportation problem to select a new type of coal for a steel manufacturing unit. Top 15, 114–137 (2007)
Hitchcock F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224–230 (1941)
Isermann H.: The enumeration of all efficient solutions for a linear multi-objective transportation problem. Naval Res. Logist. Quart. 26, 123–139 (1979)
Kumar, A., Kaur, A.: Methods for solving unbalanced fuzzy transportation problems, Operat. Res. Int. J. doi:10.1007/s12351-010-0101-3
Pramanik S., Roy T.K.: Multiobjective transportation model with fuzzy parameters: priority based fuzzy goal programming approach. J. Transp. Syst. Eng. Inform. Technol. 8, 40–48 (2008)
Ringuest J.L., Rinks D.B.: Interactive solutions for the linear multiobjective transportation problem. Eur. J. Oper. Res. 32, 96–106 (1987)
Sherali H.D., Desai J.: A global optimization RLT-based approach for solving the fuzzy clustering problem. J. Glob. Optim. 33, 597–615 (2005)
Slowinski, R.: Fuzzy multi-objective linear programming FMOLP. In: Floudas, C.A., Pardalos, P.M. Encyclopedia of Optimization, pp. 1102–1112. Springer, New York (2009)
Zadeh L.A.: Fuzzy sets. Infor. Control 8, 338–353 (1965)
Zhang G., Lu J.: Fuzzy bilevel programming with multiple objectives and cooperative multiple followers. J. Glob. Optim. 47, 403–419 (2010)
Zimmermann H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1, 45–55 (1978)
Zopounidis, C., Pardalos, P.M., Baourakis, G. (eds): Fuzzy Sets in Management. Economics and Marketing, World scientific publishing, Singapore (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gupta, A., Kumar, A. & Kaur, A. Mehar’s method to find exact fuzzy optimal solution of unbalanced fully fuzzy multi-objective transportation problems. Optim Lett 6, 1737–1751 (2012). https://doi.org/10.1007/s11590-011-0367-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-011-0367-2