Automation: How can I dispense thousands of paper sheets?
Amazon has had very good success implementing physical memory caching algorithms in their warehouses. An operating system can map commonly accessed data in fast to access locations(near the centre of the platter) and near each other to reduce travel time. Amazon found that sorting their warehouses so that commonly access items are closer and near each other has a significant increase in efficiency.

You could organize your stock in such a way. This optimization is difficult to apply after the fact, it is primarily based on where you choose to store things.

While this is not "automation" it is an optimization that might help. I think you will find actual mechanical handling of paper from shelves unrealistic cost wise unless you have a massive scale to justify it.