Interval Solution for Generalized Linear-Fractional Optimization Problems with Interval Parameters

Generalized linear-fractional optimization refers to the maximization (minimization) of the minimum (maximum) value over a finite set of linear-fractional objective functions subject to linear constraints. We address generalized linear-fractional problems with interval parameters both in the objective functions and the constraints. By introducing consistency checks for systems of linear inequalities, we show that the endpoints of the interval that contains the optimal value of an arbitrary instance of the interval problem are the optimal values of exactly two deterministic generalized linear-fractional problems. Illustrative applications demonstrate the characteristics and the numerical performance of the proposed solution method.