An interactive method of tackling uncertainty in interval multiple objective linear programming

Mathematical programming models for decision support must explicitly take account of the treatment of the uncertainty associated with the model coefficients along with multiple and conflicting objective functions. Interval programming just assumes that information about the variation range of some (or all) of the coefficients is available. In this paper, we propose an interactive approach for multiple objective linear programming problems with interval coefficients that deals with the uncertainty in all the coefficients of the model. The presented procedures provide a global view of the solutions in the best and worst case coefficient scenarios and allow performing the search for new solutions according to the achievement rates of the objective functions regarding both the upper and lower bounds. The main goal is to find solutions associated with the interval objective function values that are closer to their corresponding interval ideal solutions. It is also possible to find solutions with non-dominance relations regarding the achievement rates of the upper and lower bounds of the objective functions considering interval coefficients in the whole model.