A class of linear interval programming problems and its application to portfolio selection

This paper discusses a class of linear programming problems with interval coefficients in both the objective functions and constraints. The noninferior solutions to such problems are defined based on two order relations between intervals, and can be found by solving a parametric linear programming problem. Considering the uncertain returns of assets in capital markets as intervals, we propose a model for portfolio selection based on the semiabsolute deviation measure of risk, which can be transformed to a linear interval programming model studied in the paper. The method is illustrated by solving a simplified portfolio selection problem.