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In reference to the first question, I think it often comes down to the information you have about the underlying uncertainty. If you only have intervals or ranges, robust is the way to go. If you have all of the distributional information (or assume it), stochastic programming is an option. As @TheSimpliFire mentioned, you can include risk measures in ...

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The following papers discuss this extensively with numerical experiments, but they tackle specific examples. Emphasis is mine. Kazamzadeh et al. (2017) This is a comparison of the two techniques using the example of unit commitment, answering your first question. A popular impression has arisen that the robust approach, with its focus on the worst case, is ...

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What you’re describing is known as inventory optimization under yield uncertainty. There is quite a bit of literature on it. Two relevant literature reviews are Yano and Lee (OR 1995) and Grosfeld-Nir and Gerchak (AOR 2004). Yield uncertainty is only one type of supply uncertainty. A closely related form is disruptions; my students and I wrote a review ...

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The following is purely personal opinion. I would say a (substantial) majority of non-academic optimization problems do not involve any of the methods you listed, for a number of reasons. "Better is the enemy of good enough." Using fixed, plausible values for parameters and ignoring uncertainty often produce answers that are good enough for ...

9

Regarding your first question, I think other answers have summed it up pretty good. Two things I would add are as follows: Stochastic programming models (besides chance constraint/probabilistic programming ones) allow you to correct your decision using the concept of recourse. In this idea, you have to make some decisions before the realization of uncertain ...

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There are many ways to approach your problem and there is a lot of literature on similar problems. You could look at the following article: Gorissen, Bram L., et al. “A Practical Guide to Robust Optimization.” Omega, vol. 53, June 2015, pp. 124–37. ScienceDirect, https://doi.org/10.1016/j.omega.2014.12.006. A simple approach would be to add 'safety slack' ...

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There are many applications of different MCDM (Multi-Criteria Decision Making) method families when there is some kind of uncertainty in weights or amount of objectives or criteria. Mosadeghi et al. (1), in their paper, explained the dimensions of uncertainty in the MCDM problems as follow: the location of uncertainty – where the uncertainty manifests ...

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After having read Chapter 5.3 of Decision Making Under Uncertainty by Mykel J. Kochenderfer, I have come to some conclusions. We are dealing with model uncertainty, in which case we can formulate a Bayes Adaptive Model. In the book that I read, the term model uncertainty refers more to not knowing what the transition probabilities nor the structure of the ...

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How to generate a multivariate Gaussian? It must be answered somewhere on Cross Validated, but I cannot find it now, some comments at https://stats.stackexchange.com/questions/341805/are-mvrnorm-in-mass-r-package-and-rmvn-in-mgcv-r-package-equivalent/341808#341808. Let $X \sim \mathcal{N}(\mu, \Sigma)$ and $\epsilon \sim \mathcal{N}(0,I)$. Then we can ...

2

The issue you are describing has to do with the necessity of accounting for both short- and long-term dynamics in a decision problem under uncertainty, or in general uncertainty at different levels of resolution. There are two issues here. The practical implementation of a stochastic program lives on a scenario tree. So the first issue is how to arrange ...

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Stochastic Optimization (SO) requires the probability distributions (PDF) of the uncertain variables which are usually hard to fit. Then, a large number of scenarios are required to be sampled from these PDFs with their probabilities. This makes some computational complexities and intractability so, scenario reductions are needed but some information will be ...

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