Using necessarily weak ecient solutions for solving a biobjective transportation problem with fuzzy objective functions coecients

This paper considers a biobjective transportation problem with various fuzzy objective functions coecients. Fuzzy coecients can be of dierent types such as triangular, trapezoidal, (semi) L 􀀀 R, or at (semi) L 􀀀 R fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using -cuts of fuzzy coe- cients. Then, we consider a x -cut and obtain a necessarily weak ecient solution to the yielded interval biobjective program by a new algorithm. It uses basic feasible solutions and the parametric simplex algorithm. Furthermore, we suggest another algorithm for nding a reasonable solution, called -necessarily weak ecient, to the main biobjective transportation problem. To illustrate the validity and performance of the proposed algorithms, we present some numerical examples.