A Theory of Constraints (TOC) advocate visits your factory and seems bemused by your use of EOQ to set your batch sizes. You launch into a brilliant defense of the EOQ

The TOC advocate grabs a piece of chalk and proceeds to sketch two sets of inventory cost curves on your pristine shop floor. What will his two different sets of cost curves look like and why?

One possible problem with your use of EOQ might arise if the TOC advocate (or the student answering the question) has read the supplement on special inventory models and realizes that production rate and consumption rate should be used to tweak the basic EOQ analysis. If the TOC disciple and the students haven't read that section, then their analysis should proceed as follows.
The two sets of curves will have radically different values for S (setup cost) depending on whether they represent bottleneck machines or non-bottlenecks. A bottleneck machine will have an absurdly high S since it governs flow (and ultimately profit) for the entire plant. A non-bottleneck machine will have a miniscule S since it has excess capacity and can be idle for some time with no real impact on throughput. The high S will dictate larger lot sizes and provide significant pressure to reduce setup times; the low S will dictate small lot sizes and no pressure to reduce setup times.