Abstract

In this paper, a solution procedure has been given for the Chance Constrained Programming Models For Multi-Objective Interval Solid Transportation Problem under stochastic environment (MOISTP) where the cost coefficients of the objective functions, 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

References

• Alefeld, G. and Herzberger, 1983 J. Introduction to Interval computations, Academic Press, New York.
• Liu, B. 2002 Theory and Practice of Uncertain Programming, Physica-Verlag, New York.
• R.E.Moore, M.E. 1979 Method and Applications of Interval Analysis, SLAM, Philadephia, PA.
• Shell, E. 1955 Distribution of a product by several properties, Directorate of Management Analysis, Proc. 2nd Symp. on Linear programming, Vol. 2, pp. 615-642, DCS/Comptroller H.Q. U.S.A.F., Washington, DC.
• Basu, M., Pal, B.B., and Kundu, A., 1994 An algorithm for optimum solution of solid fixed charge transportation problem , Optimization 31 , 283-291.
• Bit, A.K, Biswal, M.P. and Alam, S.S. 1993 Fuzzy programming approach to multi-objective solid transportation problem, Fuzzy Sets Systems. 57, 183-194.
• Baoding Liu and Yian-Kui Liu, AUG 2002 Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10(4) 445-450.
• Charnes, A. and Cooper, W.W. 1952 Chance-constrained and normal deviates. Journal of American Statistics Association 57, 134-118.
• Charnes, A. and Cooper, W.W. 1959 Chance-constrained programming. Management Science 6 (1), 73-80.
• Charnes, A. and Cooper, W.W., 1963 Deterministic equivalents for optimizing and satisfying under chance constraints, Operations Research 11, 18-39.
• Das,S.K., Goswami, A. and .Alam, S.S. 1999 Multi-objective transportation problem with intervsl cost, source and destination parameters, European Journal of Operations Research 117, 100-112.
• Gen, M. Ida, K., Y.Li,Y. and Kubota, E. 1995 Solving bicriteria solid transportation problem with fuzzy numbers by a genetic algorithm, Comput. Ind. Eng. 29, 537-541.
• Ishibuchi, H. and Tanaka, H. 1990 multiobjective programming in optimization of the interval objective function, European Journal of Operations Research 48, 219-225.
• Inguichi, M. and Kume, Y. 1991 Goal programming problem with interval coefficient and target intervals, European Journal of Operations Research 52 , 345-360.
• Jimenez, F and Verdegay, J.L. 1998 Uncertain solid transportation problems, Fuzzy sets systems. 100, 45-57.
• Jimenez, F. and Verdegay, J.L. 1999 Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach, European Journal of Operations Research, 117, 485-510.
• Li, Y., .Ida, K., Gen, M. and R.Kobuchi, R. 1997 Neural network approach for multi-criteria solid transportation problem, Comput. Ind. Eng. 33, 465-468.
• Li, Y., Ida, K. and M.Gen, M. 1997 Improved genetic algorithm for solving multi-objective solid transportation problem with fuzzy numbers, Comput. Ind. Eng. 33, 589-592.
• Lixing Yang and Linzhong Liu, 2007 Fuzzy fixed charge solid transportation problem and algorithm , Applied soft computing , 7, 879-889.
• Lixing Yang, Yuan Feng, 2007 A bi-criteria solid transportation problem with fixed charge under stochastic environment, Applied Mathematical Modeling 31, 2668-2683.
• Liberling, H. 1981 On finding compromise solutions for multicriteria problems using the fuzzy min-operator, Fuzzy Sets and Systems 6, 105-118.
• Liu, B. and Iwamura, K. 1998 Chance constrained programming with fuzzy parameters. Fuzzy Sets Systems. 94 (2), 227-237.
• Nagarajan, A. and Jeyaraman, K. March 2009-May 2009 Mathematical modeling of solid fixed cost bi-criterion indefinite quadratic transportation problem under stochastic environment, Emerging journal of engineering science and technology, Volume-02, N-03, pp.106 – 127.
• Nagarajan, A. and Jeyaraman, K, Solution of expected value model for multi-objective interval solid transportation problem under stochastic environment using fuzzy programming approach, Emerging journal of engineering science and technology. Article in press.
• Nagarajan, A.and Jeyaraman, K. Chance constrained goal programming models for multi-objective interval solid transportation problem under stochastic environment, International journal of applied mathematics analysis and applications. Article in press.
• Stuer, R.E. 1981 Algorithm for linear programming problems with interval objective function coefficient, Mathematics of Operations Research 6 , 333-348.
• Tong, S. 1994 Interval number and fuzzy number linear programming, Fuzzy Sets and Systems 66, 301-306.
• Zadeh, L.A. 1965 Fuzzy sets, Information and control 8, 338-353.
• Zimmerman, J. 1978 Fuzzy programming and Linear programming with several objective functions, Fuzzy Sets and Systems 1, 45-55.