One Point Conventional Model to Optimize Trapezoidal Fuzzy Transportation Problem

This article puts forward a new one point approach to optimize trapezoidal fuzzy transportation problem. It proposes the method having point wise breakup of the trapezoidal number in such a way, that fuzzy transportation problem is converted into four crisp transportation problems. The method is equipped with minimum of supply and demand approach. In the end, the solutions are combined to construct the optimal solution. Modified distribution is applied on each crisp problem to develop optimal solution. The scheme presented is compared with competitive methods available in literature and it is found to be in good coordination with these. The scheme is equally good to be applied on unbalanced problems. Two numerical problems are considered to test the performance of the proposed approach. KeywordsOne point approach, Trapezoidal fuzzy number, Minimum demand supply, Modified distribution, Fuzzy transportation problem.

[1]  Emrah Akyar,et al.  A New Method for Ranking triangular Fuzzy numbers , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[2]  Hans-Jürgen Zimmermann,et al.  Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems , 2000, Fuzzy Sets Syst..

[3]  Salim Rezvani.  Ranking Generalized Trapezoidal Fuzzy Numbers with Euclidean Distance by the Incentre of Centroids , 2013 .

[4]  Dinesh C. S. Bisht,et al.  A unique conversion approach clubbed with a new ranking technique to optimize fuzzy transportation cost , 2017 .

[5]  Dinesh C. S. Bisht,et al.  An aggregated higher order fuzzy logical relationships technique , 2019 .

[6]  Ali Ebrahimnejad,et al.  New method for solving Fuzzy transportation problems with LR flat fuzzy numbers , 2016, Inf. Sci..

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

[8]  Phool Singh,et al.  A Unique Computational Method for Constructing Intervals in Fuzzy Time Series Forecasting , 2018 .

[9]  Dinesh C. S. Bisht,et al.  Trisectional fuzzy trapezoidal approach to optimize interval data based transportation problem , 2020 .

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

[11]  Mangey Ram,et al.  Role of Fuzzy Logic in Flexible Manufacturing System , 2018 .

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

[13]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[14]  A. H. Ganesh,et al.  Ranking of Fuzzy Numbers using Radius of Gyration of Centroids , 2013 .

[15]  Nirbhay Mathur,et al.  Trapezoidal fuzzy model to optimize transportation problem , 2016, Int. J. Model. Simul. Sci. Comput..

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

[17]  Pankaj Srivastava,et al.  Recent Trends and Applications of Fuzzy Logic , 2019, Advanced Fuzzy Logic Approaches in Engineering Science.

[18]  T. Allahviranloo,et al.  SOLVING FULLY FUZZY LINEAR PROGRAMMING PROBLEM BY THE RANKING FUNCTION , 2008 .

[19]  Robert John,et al.  Soft Computing Techniques and Applications , 2021, Advances in Intelligent Systems and Computing.

[20]  Mehdi Dehghan,et al.  Computational methods for solving fully fuzzy linear systems , 2006, Appl. Math. Comput..

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

[22]  James J. Buckley,et al.  Multi-objective Fully Fuzzified Linear Programming , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[23]  Dorota Kuchta,et al.  A concept of the optimal solution of the transportation problem with fuzzy cost coefficients , 1996, Fuzzy Sets Syst..

[24]  Dinesh C. S. Bisht,et al.  Ranking approach based on incenter in triangle of centroids to solve type-1 and type-2 fuzzy transportation problem , 2019 .

[25]  Dorota Kuchta,et al.  Fuzzy integer transportation problem , 1998, Fuzzy Sets Syst..

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

[27]  Ebrahim Nasrabadi,et al.  A mathematical-programming approach to fuzzy linear regression analysis , 2004, Appl. Math. Comput..

[28]  Pankaj Srivastava,et al.  Optimization of species transportation via an exclusive fuzzy trapezoidal centroid approach , 2019 .

[29]  Pankaj Srivastava,et al.  An efficient fuzzy minimum demand supply approach to solve fully fuzzy transportation problem , 2019 .

[30]  Ramesh C. Jain.  A procedure for multiple-aspect decision making using fuzzy sets , 1977 .

[31]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[32]  Pankaj Srivastava,et al.  Fuzzy Optimization and Decision Making , 2019, Advanced Fuzzy Logic Approaches in Engineering Science.

[33]  Pankaj Srivastava,et al.  A pioneer optimization approach for hexagonal fuzzy transportation problem , 2019 .

[34]  Amit Kumar,et al.  Methods for solving unbalanced fuzzy transportation problems , 2012, Oper. Res..

[35]  James J. Buckley,et al.  Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming , 2000, Fuzzy Sets Syst..

[36]  Phool Singh,et al.  Real coded genetic algorithm for fuzzy time series prediction , 2017 .

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

[38]  Dinesh C. S. Bisht,et al.  Particle swarm optimised fuzzy method for prediction of water table elevation fluctuation , 2018, Int. J. Data Anal. Tech. Strateg..

[39]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[40]  Pankaj Srivastava,et al.  Dichotomized Incenter Fuzzy Triangular Ranking Approach to Optimize Interval Data Based Transportation Problem , 2018, Cybernetics and Information Technologies.

[41]  Nirbhay Mathur,et al.  Algorithms for solving fuzzy transportation problem , 2018, Int. J. Math. Oper. Res..

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

[43]  R. Yager.  ON CHOOSING BETWEEN FUZZY SUBSETS , 1980 .

[44]  T. Allahviranloo,et al.  Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution , 2009 .

[45]  M. Ghazanfari,et al.  A new approach to solve time–cost trade-off problem with fuzzy decision variables , 2009 .

[46]  Adil Baykasoglu,et al.  A direct solution approach to fuzzy mathematical programs with fuzzy decision variables , 2012, Expert Syst. Appl..

[47]  P. Pandian,et al.  A New Method for Finding an Optimal Solution of Fully Interval Integer Transportation Problems , 2010 .

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