Interval linear fractional programming: optimal value range of the objective function

In the real world, some problems can be modelled by linear fractional programming with uncertain data as an interval. Therefore, some methods have been proposed for solving interval linear fractional programming (ILFP) problems. In this research, we propose two new methods for solving ILFP problems. In each method, we use two sub-models to obtain the range of the objective function. In the first method, we introduce two sub-models in which the objective functions are non-linear and the two sub-models have the largest and smallest feasible regions; therefore, the optimal value range of the objective function has been obtained. In the second method, two sub-models have been proposed in which the objective functions are linear and the optimal value of the objective function lies in the range obtained from the first method. We use our approaches to maximize the ratio of the facilities optimal allocation to the non-return fund in a bank.