Decision making under uncertainty: Is sensitivity analysis of any use?

Sensitivity analysis, combined with parametric optimization, is often presented as a way of checking if the solution of a deterministic linear program is reliable – even if some of the parameters are not fully known but are instead replaced by a best guess, often a sample mean. It is customary to claim that if the region over which a certain basis is optimal is large, one is fairly safe by using the solution of the linear program. If not, the parametric analysis will provide us with alternative solutions that can be tested. This way, sensitivity analysis is used to facilitate decision making under uncertainty by means of a deterministic tool, namely parametric linear programming. We show in this note that this basic idea of stability has little to do with optimality of an optimization problem where the parameters are uncertain.