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Year 2016, Volume: 4 Issue: 4, 114 - 127, 31.12.2016

Abstract

References

  • 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.

A Fuzzy programming approach for interval multiobjective solid transportation problem

Year 2016, Volume: 4 Issue: 4, 114 - 127, 31.12.2016

Abstract

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.

References

  • 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.
There are 19 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hasan Dalman

Publication Date December 31, 2016
Published in Issue Year 2016 Volume: 4 Issue: 4

Cite

APA Dalman, H. (2016). A Fuzzy programming approach for interval multiobjective solid transportation problem. New Trends in Mathematical Sciences, 4(4), 114-127.
AMA Dalman H. A Fuzzy programming approach for interval multiobjective solid transportation problem. New Trends in Mathematical Sciences. December 2016;4(4):114-127.
Chicago Dalman, Hasan. “A Fuzzy Programming Approach for Interval Multiobjective Solid Transportation Problem”. New Trends in Mathematical Sciences 4, no. 4 (December 2016): 114-27.
EndNote Dalman H (December 1, 2016) A Fuzzy programming approach for interval multiobjective solid transportation problem. New Trends in Mathematical Sciences 4 4 114–127.
IEEE H. Dalman, “A Fuzzy programming approach for interval multiobjective solid transportation problem”, New Trends in Mathematical Sciences, vol. 4, no. 4, pp. 114–127, 2016.
ISNAD Dalman, Hasan. “A Fuzzy Programming Approach for Interval Multiobjective Solid Transportation Problem”. New Trends in Mathematical Sciences 4/4 (December 2016), 114-127.
JAMA Dalman H. A Fuzzy programming approach for interval multiobjective solid transportation problem. New Trends in Mathematical Sciences. 2016;4:114–127.
MLA Dalman, Hasan. “A Fuzzy Programming Approach for Interval Multiobjective Solid Transportation Problem”. New Trends in Mathematical Sciences, vol. 4, no. 4, 2016, pp. 114-27.
Vancouver Dalman H. A Fuzzy programming approach for interval multiobjective solid transportation problem. New Trends in Mathematical Sciences. 2016;4(4):114-27.