Correctly evaluating a solution method that is based on an approximate model

Suppose that in some facet of industrial engineering one is faced with a difficult mathematical optimization problem based on an accurate model of the practical situation under consideration. One approach often used is to determine a solution based upon a simpler approximate model of the problem situation. One is then, of course, interested in evaluating the degradation in the measure of effectiveness (objective function) caused by using the approximate approach instead of the exact optimization. This note addresses a conceptual error, often made by students, in attempting to carry out such an evaluation.