Trapezoidal Fuzzy Numbers for the Transportation Problem
  Transportation Problem is an important problem which has been widely studied
in Operations Research domain. It has been often used to simulate different
real life problems. In particular, application of this Problem in NP Hard
Problems has a remarkable significance. In this Paper, we present the closed,
bounded and non empty feasible region of the transportation problem using fuzzy
trapezoidal numbers which ensures the existence of an optimal solution to the
balanced transportation problem. The multivalued nature of Fuzzy Sets allows
handling of uncertainty and vagueness involved in the cost values of each cells
in the transportation table. For finding the initial solution of the
transportation problem we use the Fuzzy Vogel Approximation Method and for
determining the optimality of the obtained solution Fuzzy Modified Distribution
Method is used. The fuzzification of the cost of the transportation problem is
discussed with the help of a numerical example. Finally, we discuss the
computational complexity involved in the problem. To the best of our knowledge,
this is the first work on obtaining the solution of the transportation problem
using fuzzy trapezoidal numbers.
