You are not allowed to have children. The population has to be carefully controlled. How exactly do you plan to enforce that? Forced sterilization? Forced abortion?
We already have birth control techniques. I would presume something similar is used to choose when children are born.
Also, since it's a closed system, any child born is replacing an adult who has died. So when Bob the Engineer dies, Suzie gets to be born and she has zero choice.
This is probably overstated. In general, we need a stable population, yes. In a practical workforce sense, a child born today is replacing someone who dies 20 years later. But that does not mean that each child specifically replaces their own parent. In fact, quite the opposite - the kid's parents are probably still alive when they enter the workforce on the ship.
We are talking about a ship that has to carry a viable breeding population of humans - we are probably talking thousands of individuals. This is a town or city flying through space. There is (and, I daresay needs to be) some wiggle room as to who does what, so long as we have enough of everything. Honestly, in all likelihood, you *don't* have the situation where every individual is essential to ship operations. Most of the people on board are just folks - you fly with greater human capacity than you need, in part so that things like this are not an issue. Take 10,000 people with you, and enough will have the aptitudes you need in essential crew. The rest are passengers.
And, [MENTION=177]Umbran[/MENTION] (sorry about the errr... slip of the keyboard there. Little frustration boiled through. Won't happen again.) you talked about innovation. What innovation? You are in a closed system with little spare resources and no outside information coming in. How, exactly, are you going to innovate? You cannot afford experimentation.
Quite the opposite - you *NEED* experimentation. The idea that people on Earth thought of everything before you left is ludicrous. The idea that you cold *stop* human innovation on the scale of generations is also nonsensical. People on the ship will have new ideas. People on Earth will have new ideas, and will transmit them to the ship!
"Experimentation" does not mean "put a new idea into production use without testing." But, even today, we make changes to spacecraft after flight has begun - most frequently in software. A friend of mine used to work for NASA doing software updates for craft that had gyroscopes fail, among other things, to keep a craft at least somewhat functional when physical systems no longer function. Here's an article on an example of software upgrades to spacecraft:
http://blogs.esa.int/rosetta/2014/03/28/software-upgrade-at-655-million-kilometres/
Darned tootin' if we were present, you'd see us replacing physical parts, too.
Did you see
The Martian? The bits where Matt Damon's character communicates with Earth, and they come up with plans and changes to help him survive? That's not implausible.
You leave Earth *with* spare resources, and the ability to recycle. Every part of the ship needs to be replaceable, and you need to be able to make new parts. You have redundant systems so that you can have one down while you repair or upgrade another. You may have the idea that the ship must be static - get that out of your head. The only things humans build that last for centuries unchanged are piles of stone. This thing must be dynamic. Change is part of the plan.
