Then that mechanic should not be in the game in the first place
its not about mechanics. its about simulating a world. you start with what the world should be like, then determine what level of depth of simulation you need for things to be believable. then you come up with a model for what you want to simulate, which then leads to "how it works", which some folks might call a "game mechanic". But some things you simulate aren't necessarily fun, such as crossing off a day of food in a table top rpg. Computers are there to do the mundane simulation for us, so we can get on with the cool stuff, and its all still seems realistic and believable.
Its natural to want to have mine production related to factory production. that's how things work in the real world, and how one might expect them to also work in a 4X. But just because you want to simulate some effect, doesn't mean you necessarily have to build a gameplay mechanic around it. simulation of things that include real choices with no dominant strategy add game play value. simulation of other things - such as "swords do damage points which reduce hit points" vs "any hit kills" add believably. after all, games would be kind of weird if one didn't simulate damage. but combat is the game play value there. damage modeling is just a book keeping chore for the computer to handle for us. resource gathering and distribution is a similar case to damage modeling. its modeling a lower level detail that adds believably to game play.
so where does that leave you? i'll assume you like the concept of mines and factories being related. so you start with a model like:
1. mine output is a function of available labor plus perhaps a few other variables such as how easy the stuff is to mine, tech level of mining equipment used, etc.
2. factory output is a function of available labor and mine output, plus any other appropriate variables.
so the player will need to build factories to produce stuff, and build mines to produce raw materials for factories.
but micro-managing building mines is "no fun".
so you have your "Ministry of Mines" to do it for you - you DO have a Ministry of Mines don't you? I mean, after all, you're the Galactic Emperor! <g>.
of course the Galactic Empire should have empire wide mineral reserves that roll over from turn to turn, and of course there should be a Ministry of Mines to attend to the details of dealing with such things which are beneath the Emperor, and of course the Emperor should be able to summon the Minister of Mines at any time and tell them to build a mine here or a factory there - cause they're the Emperor of The Galaxy!
this _is_ the kind of thing - the "aesthetic" - your shooting for, right?