Without a doubt, pops and jobs are Stellaris' biggest source of lag right now. Every month, the AI checks, for every single pop in the game, for every single trait and modifier, every single job and its candidate pops. You can imagine how intensive this gets, so much so that Paradox had to introduce population control in the 3.0 update.
What Production Revolution(PR) does is to completely get rid of that system, and condense everything into a single, easy-to-use system. Every pop is aggregated into a variable known as Manpower(representative of population) for every planet, and every job type compatible with this mod is condensed into a single job representative of the output/work of all the jobs on that planet. In short, this means that instead of checking thousands of pops for hundreds of different jobs, Stellaris only needs to do it only once.














Production Revolution should be AT THE BOTTOM - the less stuff that overwrites PR the better.



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• StellarStellaris - completely incompatible due to it changing the way modifiers are updated.
  
• Ruler Level System, Scientist Level Extension and Merged Leader Levels has some script conflicts, which leads to CTD, which may be targeted for compatibility in the future.
  
• Theory of Population Malthusian Blade 3.1.* and Species Countries - completely incompatible, they will break manpower system
  
• Vanilla job support is integrated, and anything that modifies Vanilla jobs is supported. e.g. Traits that give Metallurgists 20% bonus to Alloy production will be taken into account when PR calculates production output.
  
• Mods that add new job types need compatibility patches to work with PR, but will otherwise work just fine using the Vanilla job system.
  
• Mods that use num_pops for checks or other functionalities need compatibility patches - Because PR greatly condenses large numbers of pops, num_pops might not be accurate as a check for other mods.
  
• Here are some cusomized Compatibility Patch
  

Some Additional Tips - As mentioned here, by minimizing sections of your outliner (i.e. Planets, Military Ships, Armies etc.), you'll be able to further increase game speed immensely.