When looking at optimization under uncertainty, do you more often use robust optimization (parameters are known within some bounds), or stochastic programming (parameters follow a known distribution)? asked 20 Jun '12, 05:33 jfpuget 
The main issue to consider for making such decision is that which approach better suits your problem definition and available data. Hence, the answer is problemdependent. However, some arguments could be made in favor of robust optimization from a (very) practical point of view.
Therefore, I believe robust optimization is more applicable in most common situations. answered 20 Jun '12, 06:02 Ehsan ♦ Thanks. You're saying that building the distribution requires more data hence makes stochastic programming less likely to be relevant. Is the quote from you or from someone else?
(20 Jun '12, 22:17)
jfpuget
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Not necessarily. For example, if your designing a supply chain from the scratch, usually many factors like demand and prices are unknown and there is limited enough data to fit a probability distribution function. However, if you're redesigning a currentlyavailable supply chain, you usually have enough data to fit distributions for the parameters you need. In summary, it depends on your system type and how long it's been working. Sorry, I forgot to add the link. It's from a paper authored by my colleagues and myself. There, we have briefly compared these methods within a SCM context.
(20 Jun '12, 23:53)
Ehsan ♦
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Another thought on the question: Robust optimization models are, by nature, usually designed for riskaverse decisionmaking (one exception is uncertainty budget model by Bertsimas and Sim), while stochastic programming models are more versatile in that area as you have more options on how to define the recourse function. This is an important plus for stochastic programming.
(23 Jun '12, 02:20)
Ehsan ♦

I agree that the answer is problem dependent. In my own experience, I have found that both stochastic and robust models have been roughly equally useful in logistics applications. I also think that it is typically much more difficult to build the right model that incorporates uncertainty, compared to cases where one chooses to build a deterministic model. Here are some ideas I try to keep in mind when modeling that may help lead to an appropriate model:
answered 21 Jun '12, 10:51 Alan Erera Alan, thanks. I fully agree although you do not answer my question!
(04 Jul '12, 20:12)
jfpuget
Jean Francois, I more often formulate 2stage expected value minimization models that could theoretically be solved as exact stochastic integer programs, but find solutions to those models via heuristics. When I formulate robust optimization models, I tend to solve them exactly with IP codes.
(05 Jul '12, 11:38)
Alan Erera

When modeling uncertainty as bounds on a random variable you're implicitly assuming that everything outside those bounds will have probability 0. It's a pretty strong statement to make in some cases, especially because the consequences of unforeseen deviations (the infamous "black swans") can be catastrophic. On a more technical note, the results of robust optimization apply for some very well defined cases, e.g. logconcave distributions over convex sets and specific (e.g. LP) structure of the optimization problem. answered 08 Mar '16, 10:02 ocramz 