The CPU is an Intel(R) Core(TM) i7-3770K CPU @3.50GHz, the machine has 32 GB of memory, and the video card is an AMD Radeon (TM) R7 370 Series.

However, I do not believe the problem is the hardware because I can double-click on a core world and the screen for managing the world pops right up, but when I double-click on a shipyard it takes much longer for the screen for managing the shipyard to appear.  The slow speed gets worse as you build more shipyards so I suspect the problem is in the logic used to assemble the contents that are to appear in the management screen.

What is much worse than the shipyard management screen is clicking on the "+" icon to design a ship.  The shipyard management screen disappears and it is about 5 seconds before the ship design screen appears.  From that screen, when you click on the "+" icon to design a completely new ship it is another 5 seconds before the screen to design a new ship appears.  Exiting the designer screen is also very slow.  Again, the problem gets worse as you go through the game.  It is not bad when you start a new game, but it is almost intolerable as you get near the end of the game.

I suspect that, if you have a save of a game that has over 25 shipyards, you should be able to duplicate what I am describing.

Update:  I just completed a tiny galaxy and I did not have any speed issues with shipyards.  This would imply that the software has some kind of issue that crops-up as the galaxy size increases.  Perhaps the way collections are designed and/or accessed could be the cause.  I used to design and write multi-threaded object-oriented software that made extensive use of collections so I am very aware of the performance issues that arise when collections are not designed and used efficiently.