12
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Modeling the uncertainty of the input parameters
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 ...
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10
votes
Accepted
How is optimization under uncertainty done in real world applications?
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.
"...
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10
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Modeling the uncertainty of the input parameters
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 ...
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9
votes
Safety stock when there is uncertainty in order completion
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 ...
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9
votes
Accepted
Modeling the uncertainty of the input parameters
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 ...
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6
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How to cope with the rigidity of solutions?
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 ...
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6
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Families of methods to deal with criterion uncertainties in multicriteria decision analysis
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. (...
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5
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Robust optimization for IP formulation
I think this is a relatively easy but still general paper to start with: https://arxiv.org/pdf/1501.02634.pdf
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4
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Model or State Uncertainty in Queueing Model due to uncertain arrival rate
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 ...
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3
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Can stochastic dual dynamic programming algorithm (or any variant of it) handle multi-stage optimization problems with here-and-now uncertainty nodes?
Here-and-now uncertainty problems, which are also known as Decision-Hazard problems, are problems that decisions need to be made before the revelation of uncertain parameters on each node of a ...
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How to approximate an uncertain constraint?
Yes, it is always mathematically guaranteed that $$\sum_i \min_\theta a_{i, \theta} ≤ \min_\theta \sum_i a_{i, \theta} \tag{1}$$ and that $$\sum_i \max_\theta a_{i, \theta} ≥ \max_\theta \sum_i a_{i, \...
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3
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How to generate correlated samples?
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-...
2
votes
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How to generate correlated samples?
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 ...
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2
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Modeling the uncertainty of the input parameters
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 ...
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2
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How to approximate an uncertain constraint?
My simple logic says your constraint states that the lowest of the lhs should always be greater than/equal to the highest values possible in the rhs within the given interval. If you take sum then you ...
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2
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Robust optimization for IP formulation
you may check this https://pubs.acs.org/doi/full/10.1021/ie200150p ,there are two other papers related to that, II and III, I hope you will find it useful.
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1
vote
Shortest path problem with time as a random variable with correlation
Disclaimer: My response is not meant to be an exhaustive list of relevant directions \ publications for the $\alpha$-reliable shortest path problem, but here are a few papers on related problems that ...
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1
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Number of scenarios in non-deterministic optimization methods
Generally if aiming for robust I'd try to get scenarios that would fall within 95% (95th percentile if distribution is discrete) of cases or choose the worst-case scenarios. Depending upon ...
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