I imagine Kellhus and his ProbTrance, plus Imperial planners, came up with the minimum amount of sorcerers / warriors needed to take down Golg. and the Consult.
I'm not so sure about that. Golgotterath and its resources are pretty unknown. I think they were more likely to try and maximize everything so that they got the most possible to the gates. Schoolmen first, obviously, the more the better, soldiers second. An optimal solution for that equation probably goes something like: the more schoolmen that live, the less risky they are in the field, the more soldiers will die - but if the schoolmen are too cautious and too many soldiers die, then all of them die as well.
Then, calculate how big the host, that is the Ordeal, should be, in order to ensure this minimum amount completes the journey and their mission.
I love the section in TJE where they talk about all the logistics planning. Basically 20 years to assemble all the food and infrastructure behind sending an army across the world.
Yet, how would Kellhus have enough info to arrive at these numbers?
I mean, has he or someone else done some extensive reconnaissance / fact-finding?
The imperial trackers, for one. They spent a lot of time sending out people to meticulously map out the land as far as they could go. Not all the way to Golgotterath, but they got pretty far.
All the scalpers pushing back the sranc would have helped some as well.
Ancient Mandate texts - IIRC Kellhus spent some time going through their entire library trying to glean every piece of information about his foe that he could.
Kellhus himself probably did some hopping around too.
But like I said above, I don't they they were really solving the equation for a minimum, but a maximum. The max food they could carry, the max causalities they could suffer, the max attrition, etc. etc. They may have come up with a minimum they thought they needed, but really, their goal would have been to get the max forces their possible.