An Approach to Solve a Possibilistic Linear Programming Problem

Affiliation(s)

Department of Mathematics, Delhi University, Delhi, India.

Department of Mathematics, DeenDayalUpadhyay College, Delhi University, Delhi, India.

Department of Mathematics, Delhi University, Delhi, India.

Department of Mathematics, DeenDayalUpadhyay College, Delhi University, Delhi, India.

ABSTRACT

The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.

Cite this paper

R. Chopra and R. Saxena, "An Approach to Solve a Possibilistic Linear Programming Problem,"*Applied Mathematics*, Vol. 5 No. 2, 2014, pp. 226-233. doi: 10.4236/am.2014.52024.

R. Chopra and R. Saxena, "An Approach to Solve a Possibilistic Linear Programming Problem,"

References

[1] L. A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems, Vol. 1, 1978, pp. 3-28.

[2] R. E. Bellman and L. A. Zadeh, “Decision-Making in a Fuzzy Environment,” Management Science, Vol. 17, 1970, pp. 141164.

[3] H.-J. Zimmermann, “Description and Optimization of Fuzzy Systems,” International Journal of General Systems, Vol. 2, 1976, pp. 209-215.

[4] H.-J. Zimmermann, “Fuzzy Programming and Linear Programming with Several Objective Functions,” Fuzzy Sets and Systems, Vol. 1, 1978, pp. 45-56. http://dx.doi.org/10.1016/0165-0114(78)90031-3

[5] M. L. Hussein, “Complete Solutions of Multiple Objective Transportation Problems with Possibilistic Coefficients,” Fuzzy Sets and Systems, Vol. 93, 1998, pp. 293-299.

[6] W. F. Abd El-Washed, “A Multi-Objective Transportation Problem under Fuzziness,” Fuzzy Sets and Systems, Vol. 117, 2001, pp. 27-33.

[7] Y. J. Lai and C. L. Hwang, “A New Approach to Some Possibilistic Linear Programming Problem,” Fuzzy Sets and Systems, Vol. 49, 1992, pp. 121-133.

[8] T. F. Liang, “Application of Possibilistic Linear Programming to Multi-Objective Distribution Planning Decisions,” Journal of the Chinese Institute of Industrial Engineers, Vol. 24, 2007, pp. 97-109.

[1] L. A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems, Vol. 1, 1978, pp. 3-28.

[2] R. E. Bellman and L. A. Zadeh, “Decision-Making in a Fuzzy Environment,” Management Science, Vol. 17, 1970, pp. 141164.

[3] H.-J. Zimmermann, “Description and Optimization of Fuzzy Systems,” International Journal of General Systems, Vol. 2, 1976, pp. 209-215.

[4] H.-J. Zimmermann, “Fuzzy Programming and Linear Programming with Several Objective Functions,” Fuzzy Sets and Systems, Vol. 1, 1978, pp. 45-56. http://dx.doi.org/10.1016/0165-0114(78)90031-3

[5] M. L. Hussein, “Complete Solutions of Multiple Objective Transportation Problems with Possibilistic Coefficients,” Fuzzy Sets and Systems, Vol. 93, 1998, pp. 293-299.

[6] W. F. Abd El-Washed, “A Multi-Objective Transportation Problem under Fuzziness,” Fuzzy Sets and Systems, Vol. 117, 2001, pp. 27-33.

[7] Y. J. Lai and C. L. Hwang, “A New Approach to Some Possibilistic Linear Programming Problem,” Fuzzy Sets and Systems, Vol. 49, 1992, pp. 121-133.

[8] T. F. Liang, “Application of Possibilistic Linear Programming to Multi-Objective Distribution Planning Decisions,” Journal of the Chinese Institute of Industrial Engineers, Vol. 24, 2007, pp. 97-109.