Robust/Stochastic optimization deployed in real-world systems/applications

This heavily depends on the application at hand and could vary all the way from milliseconds to months. It all comes down to rigorously defining the specs.

Many parameters are in play:

• How long does your feedback loop need to be, i.e., how often does your system need to update?
• How high is the uncertainty and how does it grow over time?
• Do you know the statistical distribution of the uncertainty? If not, can you derive it with statistical confidence?
• How often does new data come in? For a chemical process that could be milliseconds, for price/demand optimisation it could be days/weeks/months.
• How frequently can your physical system actually update? For instance, in factories some machines can take two days to shut down/start up.

Unfortunately there's no silver bullet here, your team will have to do bespoke engineering work to figure out the answers to these questions and create a solution that fits the physical system. You need to derive bounds for the uncertainty and then make sure the solution is robust enough for the specs at hand.

Once you figure out the specs, the rest is simply a matter of picking the right algorithm/tools to meet said specs.