As someone who works in a custom fabrication shop and who has been research job shop scheduling for over a decade as an attempt to get better at it, it's a computationally impossible task. There are huge numbers of "optimal" ways to schedule the shop and all of them require enormous amounts of computation. Genetic algorithms are offering the most promise right now, but the schedule has to be constantly updated because things never take as long as you think they will.

This is primarily because, unlike manufacturing, the basic unit of our system is a person, with all of their chaotic outputs. You start stacking those up and you end up with "long, fat tails" in every analysis you do. Your probabilities are spread almost flat over a broad range of outcomes.

It's fascinating and definitely falls into the category of uncomputable.