Model for Solving Fuzzy Multiple Objective Problem

Affiliation(s)

Department of Mathematics, Delhi University, Delhi, India.

Department of Mathematics, Deen Dayal Upadhyay College, Delhi University, Delhi, India.

Department of Mathematics, Delhi University, Delhi, India.

Department of Mathematics, Deen Dayal Upadhyay College, Delhi University, Delhi, India.

ABSTRACT

In real world decision making problems, the decision maker has to often optimize more than one objective, which might be conflicting in nature. Also, it is not always possible to find the exact values of the input data and related parameters due to incomplete or unavailable information. This work aims at developing a model that solves a multi objective distribution programming problem involving imprecise available supply, forecast demand, budget and unit cost/ profit coefficients with triangular possibility distributions. This algorithm aims to simultaneously minimize cost and maximize profit with reference to available supply constraint at each source, forecast demand constraint at each destination and budget constraint. An example is given to demonstrate the functioning of this algorithm.

KEYWORDS

Decision Making Problems; Multi Objective Distribution Programming Problem; Fuzzy Set Theory

Decision Making Problems; Multi Objective Distribution Programming Problem; Fuzzy Set Theory

Cite this paper

R. Chopra and R. Saxena, "Model for Solving Fuzzy Multiple Objective Problem,"*American Journal of Operations Research*, Vol. 3 No. 1, 2013, pp. 65-69. doi: 10.4236/ajor.2013.31005.

R. Chopra and R. Saxena, "Model for Solving Fuzzy Multiple Objective Problem,"

References

[1] L. A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems, Vol. 1, No. 1, 1978, pp. 3-28. doi:10.1016/0165-0114(78)90029-5

[2] H.-J. Zimmermann, “Description and Optimization of Fuzzy Systems,” International Journal of General Systems, Vol. 2, No. 1, 1976, pp. 209-215. doi:10.1080/03081077508960870

[3] R. E. Bellman and L. A. Zadeh, “Decision-Making in a Fuzzy Environment,” Management Science, Vol. 17, No. 4, 1970, pp. 141-164.

[4] S. Chanas, W. Kolodziejczyk and A. Machaj, “A Fuzzy Approach to the Transportation Problem,” Fuzzy Sets and Systems, Vol. 13, No. 3, 1984, pp. 211-222. doi:10.1016/0165-0114(84)90057-5

[5] H.-J. Zimmermann, “Fuzzy Programming and Linear Programming with Several Objective Functions,” Fuzzy Sets and Systems, Vol. 1, No. 1, 1978, pp. 45-56. doi:10.1016/0165-0114(78)90031-3

[6] L. Li and K. K. Lai, “A Fuzzy Approach to the Multi-Objective Transportation Problem,” Computers and Operations Research, Vol. 27, No. 1, 2000, pp. 43-57. doi:10.1016/S0305-0548(99)00007-6

[7] M. L. Hussein, “Complete Solutions of Multiple Objective Transportation Problems with Possibilistic Coefficients,” Fuzzy Sets and Systems, Vol. 93, No. 3, 1998, pp. 293-299. doi:10.1016/S0165-0114(96)00216-3

[8] W. F. Abd El-Washed, “A Multi-Objective Transportation Problem under Fuzziness,” Fuzzy Sets and Systems, Vol. 117, No. 1, 2001, pp. 27-33. doi:10.1016/S0165-0114(98)00155-9

[9] Y. J. Lai, and C. L. Hwang, “A New Approach to Some Possibilistic Linear Programming Problem,” Fuzzy Sets and Systems, Vol. 49, No. 2, 1992, pp. 121-133. doi:10.1016/0165-0114(92)90318-X

[10] T. F. Liang, “Application of Possibilistic Linear Programming to Multi-Objective Distribution Planning Decisions” Journal of the Chinese Institute of Industrial Engineers, Vol. 24, No. 2, 2007, pp. 97-109. doi:10.1080/10170660709509025

[1] L. A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems, Vol. 1, No. 1, 1978, pp. 3-28. doi:10.1016/0165-0114(78)90029-5

[2] H.-J. Zimmermann, “Description and Optimization of Fuzzy Systems,” International Journal of General Systems, Vol. 2, No. 1, 1976, pp. 209-215. doi:10.1080/03081077508960870

[3] R. E. Bellman and L. A. Zadeh, “Decision-Making in a Fuzzy Environment,” Management Science, Vol. 17, No. 4, 1970, pp. 141-164.

[4] S. Chanas, W. Kolodziejczyk and A. Machaj, “A Fuzzy Approach to the Transportation Problem,” Fuzzy Sets and Systems, Vol. 13, No. 3, 1984, pp. 211-222. doi:10.1016/0165-0114(84)90057-5

[5] H.-J. Zimmermann, “Fuzzy Programming and Linear Programming with Several Objective Functions,” Fuzzy Sets and Systems, Vol. 1, No. 1, 1978, pp. 45-56. doi:10.1016/0165-0114(78)90031-3

[6] L. Li and K. K. Lai, “A Fuzzy Approach to the Multi-Objective Transportation Problem,” Computers and Operations Research, Vol. 27, No. 1, 2000, pp. 43-57. doi:10.1016/S0305-0548(99)00007-6

[7] M. L. Hussein, “Complete Solutions of Multiple Objective Transportation Problems with Possibilistic Coefficients,” Fuzzy Sets and Systems, Vol. 93, No. 3, 1998, pp. 293-299. doi:10.1016/S0165-0114(96)00216-3

[8] W. F. Abd El-Washed, “A Multi-Objective Transportation Problem under Fuzziness,” Fuzzy Sets and Systems, Vol. 117, No. 1, 2001, pp. 27-33. doi:10.1016/S0165-0114(98)00155-9

[9] Y. J. Lai, and C. L. Hwang, “A New Approach to Some Possibilistic Linear Programming Problem,” Fuzzy Sets and Systems, Vol. 49, No. 2, 1992, pp. 121-133. doi:10.1016/0165-0114(92)90318-X

[10] T. F. Liang, “Application of Possibilistic Linear Programming to Multi-Objective Distribution Planning Decisions” Journal of the Chinese Institute of Industrial Engineers, Vol. 24, No. 2, 2007, pp. 97-109. doi:10.1080/10170660709509025