ROBUSTNESS, REGRET, AND DISAPPOINTMENT

Proper scenario generation is needed to reduce sampling errors and successfully apply stochastic programming models. However, there may be more fundamental flaws in the approach:

• How is our information reliable when we assume a probability distribution? The best scenario generation will not help if we assume a probability distribution that has little to do with the true one. There are cases in which we have so little information, that building a full-fledged multivariate probability distribution amounts to pulling a heroic and futile stunt. The dependence between variables can be difficult to capture by a correlation matrix, as this only picks up linear dependencies. Furthermore, autocorrelation over time may also be an issue. In other words, there may be considerable uncertainty about the uncertainty model itself. In some case, all we are able to specify is an interval of sensible values for uncertain parameters, without attaching any probabilistic information.
• Even if the representation of uncertainty is adequate, we may look for a conservative solution. A solution which is good in an “average” sense may prove unacceptable in some extreme scenarios.
• Psychological research on the behavior of decision makers facing uncertainty has revealed patterns that are not fully compatible with the maximization of expected utility. Mechanisms such as regret and disappointment may lead to different decisions.

Illustrates a few issues with standard decision making procedures in a world of multiple stakeholders and subjective probabilities. In this section we just mention a couple of approaches that have been proposed to improve model-based decisions under risk.