Category: Decision Making Under Risk

When making decisions under risk and uncertainty in our lives, we rarely set up a utility function to formalize the problem we are facing. We come up with a solution but, unfortunately, sometimes we must admit that we were wrong. Indeed, disappointment and regret are emotions that we have all experienced. A discussion of disappointment… Continue reading Disappointment and regret in decision making

Robust optimization is a label that has been attached to a fairly wide variety of optimization modeling frameworks. A rather confusing feature is that “robust” may refer to our inability to represent uncertainty reliably within a probabilistic framework; alternatively, “robust” may refer to decision-makers’ attitude towards risk taking. In this section we mainly refer to… Continue reading Robust optimization

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: 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… Continue reading ROBUSTNESS, REGRET, AND DISAPPOINTMENT

Multistage stochastic programming is a very powerful modeling framework, and it can be extended to cope with risk measures like CVaR, as we have seen in Section 13.3.3. However, the approach can be only as good as the scenario tree on which it is based. Given a multivariate probability distribution characterizing uncertainty, the most obvious way… Continue reading Scenario generation for stochastic programming

To give the reader an idea of how to build nontrivial financial planning models, we generalize a bit the model formulation of the previous section, in order to account for proportional transaction costs. The assumptions and the limitations behind this extended model are the following: Some of the limitations of the model may easily be… Continue reading Asset–liability management with transaction costs

The best way to introduce multistage stochastic models is a simple asset–liability management (ALM) model.24 We have an initial wealth W0, that should be properly invested in such a way to meet a liability L at the end of the planning horizon H. If possible, we would like to own a terminal wealth WH larger than L; however, we should account properly for… Continue reading A multistage model: asset–liability management

Multistage stochastic programming formulations arise naturally as a generalization of two-stage models. At each stage, we gather new information and we make decisions accordingly, taking into account immediate costs and expected future recourse cost. The resulting decision process may be summarized as follows:23 From the point of view of time period t = 0, the decisions x1, …, xH are… Continue reading MULTISTAGE STOCHASTIC LINEAR PROGRAMMING WITH RECOURSE

Mean–risk formulations are based on the idea of trading off expected profit (or return) against a risk measure. Classical mean–variance portfolio optimization relies on an analytical representation of variance, which leads to an easy convex quadratic programming problem. This need not be the case if we choose another risk measure. Value at risk is easy… Continue reading A mean–risk formulation of the assembly-to-order problem

In Section 13.1.1 we defined EVPI, which is not only a way to price perfect information, but also a measure of the impact of uncertainty. If EVPI is low, uncertainty is not that relevant in the decision. However, EVPI is in most cases a theoretical construct, as we cannot trade the unpleasing here-and-now decision problem for the… Continue reading The value of the stochastic solution

In Section 12.2.1 we dealt with a production planning problem within an assembly-to-order (ATO) framework. There, we disregarded demand uncertainty and built a deterministic LP model. Now, in order to make the model a bit more realistic, we represent demand uncertainty by a scenario tree and adopt a two-stage stochastic linear programming framework: Of course, we cannot… Continue reading A two-stage model: assembly-to-order production planning