A Fuzzy programming approach for interval multiobjective solid transportation problem

A Fuzzy programming approach for interval multiobjective solid transportation problem

This paper presents a fuzzy programming approach for solving Interval Multiobjective Solid Transportation Problem (IMOSTP). In real world application, IMOSTP appears to be more realistic than a conventional Solid Transportation Problem (STP) as available data is uncertain. In such a problem the solution process is very complex. By applying the order relation on the intervals, it is first transformed into a crisp multiobjective solid transportation problem. After determining the individual optimal solution of each objective, a fuzzy programming approach is constructed to achieve the Pareto optimal solution of IMOSTP. Finally, a numerical example is illustrated to demonstrate the feasibility of the presented solution procedure.

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  • G.B. Dantzig (1963), Linear Programming and Extensions. Princeton University Press, Princeton Jersey.
  • Charnes A., and Cooper W. W. (1954). The stepping stone method of explaining linear programming calculations in transportation problems. Management Science, 1(1), 49-69.
  • Dalman H., Köçken, H. G., and Sivri, M. (2013). A solution proposal to indefinite quadratic interval transportation problem. New Trends in Mathematical Sciences, 1(2), 07-12.
  • Shell E. (1955). Distribution of a product by several properties, Directorate of Management Analysis. In Proceedings of the Second Symposium in Linear Programming (Vol. 2, pp. 615-642).
  • Haley K. B. (1962). New methods in mathematical programming-The solid transportation problem. Operations Research, 10(4), 448-463.
  • Jimenez F., and Verdegay J. L. (1998). Uncertain solid transportation problems. Fuzzy Sets and Systems, 100(1), 45-57.
  • Li Y., Ida K., and Gen M. (1997). Improved genetic algorithm for solving multiobjective solid transportation problem with fuzzy numbers. Computers and industrial engineering, 33(3), 589-592.
  • Li Y., Ida, K., Gen M., and Kobuchi R. (1997). Neural network approach for multicriteria solid transportation problem. Computers and industrial engineering, 33(3), 465-468.
  • Dalman H., Güzel N., and Sivri M. (2016). A Fuzzy Set-based approach to multi-objective multi-item solid transportation problem under uncertainty, Int. J. Fuzzy Syst. 18(4), 716-729. doi:10.1007/s40815-015-0081-9
  • Dalman H. (2016). Uncertain programming model for multi-item solid transportation problem. International Journal of Machine Learning and Cybernetics. doi:10.1007/s13042-016-0538-7
  • Moore R. E. (1966). Interval analysis, vol. 2. Englewood Cliffs: Prentice-Hall.
  • Moore R. E., and Fritz B.(1979) Methods and applications of interval analysis. Vol. 2. Philadelphia: Siam.
  • Ishibuchi H., and Tanaka H. (1990). Multiobjective programming in optimization of the interval objective function. European journal of operational research, 48(2), 219-225.
  • Chanas S., and Kuchta D. (1996). Multiobjective programming in optimization of interval objective functions a generalized approach. European Journal of Operational Research, 94(3), 594-598.
  • Oliveira C., and Antunes C. H. (2007). Multiple objective linear programming models with interval coefficients?an illustrated overview. European Journal of Operational Research, 181(3), 1434-1463.
  • Oliveira C., and Antunes C. H. (2009). An interactive method of tackling uncertainty in interval multiple objective linear programming. Journal of Mathematical Sciences, 161(6), 854-866.
  • Zadeh L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
  • El-Wahed, W. F. A., and Lee, S. M. (2006). Interactive fuzzy goal programming for multi-objective transportation problems. Omega, 34(2), 158-166.
  • Hossein RHS., Akrami H and Sadat HS. (2012). A multi-objective programming approach to solve grey linear programming. Grey Systems: Theory and Application, 2(2), 259-271.