The scenario tree of Fig. 14.1 may apply, e.g., to a two-stage stochastic programming problem. In a multistage stochastic programming model we have to make a sequence of decisions; a multistage scenario tree, like the one shown in Fig. 13.11, may be used to depict uncertainty. Even if we take for granted that sensible probabilities can be assigned and that no black swan is lurking somewhere, how can we be sure that our sequence of decisions will not affect uncertainty?
Example 14.3 Setting inventory levels at a retail store is a rather standard decision making problem under risk. Typically, the task requires choosing a model of demand uncertainty, which is an input to the decision procedure. However, which comes first: Our decision or demand uncertainty? Indeed, our very decision may affect uncertainty. Marketing studies show that the amount of items available on the shelves may affect demand. To see why, imagine buying the very last box of a product on a shelf, when there is plenty of a similar item just below. In this case, consumers’ psychology plays an important role, but even in a strict business-to-business problem, which need not involve such issues, an array of stockouts may be fatal to your customer demand. A naive newsvendor model may suggest a low service level because of low profit margins; since the order quantity should be the corresponding quantile of the probability distribution of demand, it will be very low as well, resulting in frequent stockouts. What such a model disregards is that the distribution itself will change as a consequence of our decision, if we offer a consistently low service level and keep disappointing customers. Even worse, this is likely to have an impact on the demand for other items as well. In practice, if a firm offers a catalogue of 1,000 items, it may well be the case that only 10% of them are profitable; the remaining ones are needed nonetheless, to support sales of profitable items.
The line we are drawing here is between endogenous and exogenous uncertainty. Standard decision models may fail to consider how decisions affect uncertainty, which is clearly relevant for sequential decision making. These issues may be exacerbated by the presence of multiple actors, possibly influencing each other by means of actions and information flows, giving rise to feedback effects. A quite relevant example of such nasty mechanisms is represented by financial markets instability and liquidity crises. We consider a couple of such stories in Section 14.6. But even if we disregard risk and uncertainty, the presence of multiple actors may have a relevant impact, as we illustrate in the next sections.
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