The description of the Hyperion Logistics System states, that it reduces the logistics cost of ships build on the planet by -1.
I've placed the HLS on Drengi and, once it was finished, began building several tiny ships. My current logistics value was 16, so I expected to be able to put 16 tiny ships in a fleet (regular logistics cost of 2 minus a reduction of 1 = new logistics cost of 1). However, I still could only put 8 in a fleet. I tested it again with small sized and cargo hulled ships, with the same result. I couldn't put any more ships than before in a fleet.
Is it possible, that the transfer of ship-production from the planet to the shipyard has something to do with this?
Also, the HLS currently provides a bonus of 0.05 per level to logistics. At the moment, the max level you could achieve for a military improvement is 6. This means, that the bonus to logistics would be at most 0.3. This isn't enough to increase the logistics value at all. I suggest, to raise the bonus to 0.5. That would mean a bonus of 3 at level 6.