Multi_Objective Solid Transportation Problem with Interval Cost in Source and Demand Parameters

Abstract : In this paper, a solution procedure has been given for the Multi-Objective Interval Solid Transportation Problem under stochastic environment where the cost coefficients of the objective functions have been taken as random variables whereas the source availability, destination demand and conveyance capacities have been taken as stochastic intervals by the decision makers. The problem has been transformed into a classical multi-objective transportation problem where the multiple objective functions are minimized by using fuzzy programming approach. Numerical examples are provided to illustrate the approach.

[1]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[2]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[4]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[5]  Tong Shaocheng,et al.  Interval number and fuzzy number linear programmings , 1994 .

[6]  Lixing Yang,et al.  A bicriteria solid transportation problem with fixed charge under stochastic environment , 2007 .

[7]  M. Gen,et al.  Solving bicriteria solid transportation problem with fuzzy numbers by a genetic algorithm , 1995 .

[8]  K. Jeyaraman,et al.  Solution of Chance Constrained Programming Problem for Multi-Objective Interval Solid Transportation Problem under Stochastic Environment using Fuzzy Approach , 2010 .

[9]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[10]  Baoding Liu,et al.  Dependent-chance programming with fuzzy decisions , 1999, IEEE Trans. Fuzzy Syst..

[11]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[12]  A. Goswami,et al.  Multiobjective transportation problem with interval cost, source and destination parameters , 1999, Eur. J. Oper. Res..

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

[14]  Mitsuo Gen,et al.  Improved Genetic Algorithm for Solving Multiobjective Solid Transportation Problem with Fuzzy Numbers , 1997 .

[15]  Manjusri Basu,et al.  An algorithm for finding the optimum solution of solid fixed-charge transportation problem , 1994 .

[16]  Mitsuo Gen,et al.  Neural network approach for multicriteria solid transportation problem , 1997 .

[17]  M. Gen,et al.  Improved Genetic Algorithm for Solving Multiobjective Solid Transportation Problem with Fuzzy Numbers , 1997 .

[18]  M. P. Biswal,et al.  Fuzzy programming approach to multiobjective solid transportation problem , 1993 .

[19]  Lixing Yang,et al.  Fuzzy fixed charge solid transportation problem and algorithm , 2007, Appl. Soft Comput..

[20]  José L. Verdegay,et al.  Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach , 1999, Eur. J. Oper. Res..

[21]  M. Inuiguchi,et al.  Goal programming problems with interval coefficients and target intervals , 1991 .

[22]  Ralph E. Steuer.  Algorithms for Linear Programming Problems with Interval Objective Function Coefficients , 1981, Math. Oper. Res..