optimization problem

This study investigates a multi-objective minimum cost flow with probabilistic objective function coefficients (Poss- MOMCF). Under using the α −cut set of the possibilistic variables, the Poss-MOMCF problem is converted into the corresponding (α-MOMCF) and hence into the (P-MOMCF) problem. A necessary and sufficient condition for investigating the α −possibly optimal solution is established. A fuzzy goal programming approach is applied to obtain the α −parametric optimal compromise solution. The stability set of the first kid under the concept of α −possibly optimal solution is characterized and analyzed without differentiability. Finally, a numerical example is given in the sake of the paper to clarify the methodology.