> Say we had various factories for producing goods around the world, and different factories requested the same inputs in different amounts. An algorithm could probably calculate how much of each input it should distribute to those factories.

That's a manufacturing planning system. Each product has a bill of materials, and all those parts have to be present before the product is assembled. Factories which make many similar products either have to have very good systems to get all the parts in the right place at the right time, or carry excessive inventories. It's not a market-based system. The main goal is minimizing stalls, where production stops due to lack of a part. The cost of stalls usually dominates the cost of the parts, because revenue is zero until the product is complete.