Quantitative Methods: An Introduction for Business Management

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Decision Making Under Risk

This chapter represents a synthesis of what we have become acquainted with so far. Decision making under uncertainty is a quite challenging topic, merging probability theory and statistics with optimization modeling. This mix may result in quite demanding mathematics, which we will avoid by focusing on fundamental concepts and a few illustrative toy examples to clarify them.

One preliminary question that we should address is: Which kind of uncertainty should we consider? In this chapter we take a rather standard view, i.e., that uncertainty may be represented by the classical tools of probability and statistics. In fact, this is not to be taken for granted, as there are quite different kinds of uncertainty. Compare the roll of a die against the production decision for a brand-new and truly innovative product. In the first case we do not know which number will be drawn, and betting on it means making a risky decision. However, we have no doubt about the rules of the game. In other words, we have a well-defined probability distribution of a random variable, and we just do not know in advance its realization. In the second case, we do not even know the probability distribution, which will be more subjective than fact-based. In extreme cases, even the very use of probabilities is questionable. It has been proposed to distinguish between decision making under risk and decision making under uncertainty. Strictly speaking, what we deal here with is decision ...