A generalized equilibrium value-based approach for solving fuzzy transportation problems with triangular fuzzy numbers

Transportation Problem (TP) is one of the most best known operational research problems, which plays an important role in many practical applications. In this paper, we first propose the concept of generalized equilibrium value of fuzzy number, and further give a comparison method for ranking fuzzy numbers, namely GEV-CM; secondly, for Fuzzy Transportation Problem (FTP) where the unit transportation cost is represented by triangular fuzzy number and supplies and demands is real numbers, we convert it into a crisp TP using GEV-CM, which can be easily solved by standard solution methods; thirdly, we show that our methods are efficient in solving the above mentioned FTP through a numerical example. Therefore, our discussions can be widely applied in many real life transportation problems for the decision makers.

[1]  Amit Kumar,et al.  A new method for solving fuzzy transportation problems using ranking function , 2011 .

[2]  Micheal OhEigeartaigh A fuzzy transportation algorithm , 1982 .

[3]  S. A. Abass,et al.  A PARAMETRIC STUDY ON TRANSPORTATION PROBLElVI UNDER FUZZY ENVIRONMENT , 2002 .

[4]  Jiuping Xu,et al.  A class of rough multiple objective programming and its application to solid transportation problem , 2012, Inf. Sci..

[5]  P. Kloeden,et al.  Metric Spaces of Fuzzy Sets: Theory and Applications , 1994 .

[6]  Reza Tavakkoli-Moghaddam,et al.  Solving a fuzzy fixed charge solid transportation problem by metaheuristics , 2013, Math. Comput. Model..

[7]  P. Pandian,et al.  A New Algorithm for Finding a Fuzzy Optimal Solution for Fuzzy Transportation Problems , 2009 .

[8]  M. Shanmugasundari,et al.  A Novel Approach for the fuzzy optimal solution of Fuzzy Transportation Problem , 2013 .

[9]  F. L. Hitchcock The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[10]  R. Goetschel,et al.  Topological properties of fuzzy numbers , 1983 .

[11]  Manoranjan Maiti,et al.  Fixed charge transportation problem with type-2 fuzzy variables , 2014, Inf. Sci..

[12]  Amarpreet Kaur,et al.  A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers , 2012, Appl. Soft Comput..

[13]  M. Chakraborty,et al.  Cost-time Minimization in a Transportation Problem with Fuzzy Parameters: A Case Study , 2010 .

[14]  Chiang Kao,et al.  Solving fuzzy transportation problems based on extension principle , 2004, Eur. J. Oper. Res..

[15]  Mohammadreza Safi,et al.  Solving fixed charge transportation problem with interval parameters , 2013 .

[16]  Amit Kumar,et al.  Application of Classical Transportation Methods for Solving Fuzzy Transportation Problems , 2011 .

[17]  Ali Ebrahimnejad,et al.  A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers , 2014, Appl. Soft Comput..

[18]  H. Zimmermann Fuzzy programming and linear programming with several objective functions , 1978 .

[19]  Hadi Basirzadeh,et al.  An Approach for Solving Fuzzy Transportation Problem , 2011 .

[20]  Amit Kumar,et al.  A new method for solving linear multi-objective transportation problems with fuzzy parameters , 2012 .

[21]  S. Chanas,et al.  A fuzzy approach to the transportation problem , 1984 .

[22]  Anupam Ojha,et al.  A transportation problem with fuzzy-stochastic cost , 2014 .