> I need examples for each type of constraint I have but instead, the tools expect me to figure out everything based on very generic examples

if your problems can be attacked by LP / MIP type stuff, there's a book "model building in mathematical programming" by Williams that has a couple dozen different optimisation problems for a range of applications, with worked examples of how to formulate a model to solve each of them. each problem will be much less complex than your real-world optimisation puzzle but if you browse through the problem descriptions you might be able to match some against parts of your situation & get ideas for how Williams would model and optimise it.

In a previous life, when I worked with solvers a lot, this was exactly my problem too: the examples in the documentation are always way too simple.

What I saw often, and this was in finance, that one or two developers gain proficiency in converting problems to a specific solver tool, and then we could never move to a different library because it would have been so much effort to relearn.

"My problem is mind-numbingly complex, like everyone else doing supply-chain optimization" brings me joy. I'll definitely reach out - would love to get your reaction to some of our new ideas.

> "each day the customer order is delayed is bad, but I also can't make things 3 months before they want it

This would be something in the objective function, I think? Assign some daily cost to having stock in inventory and a penalty per day that the "supply delivery to customer" task completes after the deadline.

IIRC ILOG solver used to have a lot of constraints that made implementing that kind of thing easier.