Does "run" the product here mean "produce"?
The manufacturing process is linear. We run the product in batches with changeovers every two, three days.

Question

Does "run" the product here mean "produce"?
The manufacturing  process is linear. We run the product in batches with changeovers every two, three days.

Answer

The word 'run' is used as a verb and a noun.
It is a simple way to say 'v. produce, manufacture, create' / 'n. the product produced, the total number of things made.'
For example:
v.  We need to run this product immediately.
n. The are no rejects in this run (no problems with the products that were produced).