Using necessarily weak efficient solutions for solving a biobjective transportation problem with fuzzy objective functions coefficients

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) L-R, or flat (semi) L-R fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using \gamma-cuts of fuzzy coefficients. Then, we consider a fix \gamma-cut and obtain a necessarily weak efficient 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 finding a reasonable solution, called \gamma^*-necessarily weak efficient, to the main biobjective transportation problem. To illustrate the validity and performance of the proposed algorithms, we present some numerical examples.

کلیدواژه ها:

Biobjective transportation problem ، inerval biobjective linear programming problem ، necessarily week efficient solution ، Fuzzy membership function ، gamma-cut