Towards Decision Making under Interval Uncertainty

In many practical situations, we know the exact form of the objective function, and we know the optimal decision corresponding to each values of the corresponding parameters xi. What should we do if we do not know the exact values of xi, and instead, we only know each xi with uncertainty -- e.g., with interval uncertainty? In this case, one of the most widely used approaches is to select, for each i, one value from the corresponding interval -- usually, a midpoint -- and to use the exact-case optimal decision corresponding to the selected values. Does this approach lead to the optimal solution to the interval-uncertainty problem? If yes, is selecting the midpoints the best idea? In this paper, we provide answers to these questions. It turns out that the selecting-a-valued-from-each-interval approach can indeed lead us to the optimal solution for the interval problem -- but not if we select midpoints