**InternationaleJournals**

**Fuzzy Transportation Problem of Trapezoidal Numbers
with Methods of Linear Programming Problems**

^{1}** Poonam Shugani, ^{2 }S.
H. Abbas and ^{3 }Vijay Gupta**

** ^{1}**Institute
for imsrastrure and human resource development vidisha (M.P.)

** ^{2}**Dept. of
Mathematics, Safia
Science college, Bhopal (M.P.)

** ^{3}**Dept. of Mathematics, UIT
RGPV, Bhopal (M.P.)

**Abstract**

There are various methods, in the literature, for determining the fuzzy optimal solution of a fuzzy transportation problem (transportation problems in which all the parameters are represented by fuzzy numbers).In [1] [2] we solve the Fuzzy transportation problem with the help of dual simplex and two phasemethod.Now we are solving a simple balanced fuzzy transportation problem of trapezoidal number with several methods of linear programming problems with the help of Tora package. We also compare the results of linear programming methods with result of Vogel Approximation Methods. Finally, we give illustrative example and their numerical solutions.

**Keywords: **Fuzzy Transportation Problem, Trapezoidal
Numbers, Methods of linear Programming Problems, Tora package.

**International
eJournal of Mathematics and Engineering**

**Volume 3,
Issue ****3,** **Pages: 1635 - 1641**