is research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. rough the use of the α-level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker's choice between intervals. .e maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.