Re: women and children first
In the real world, market forces lower the cost and increase the availability of commodities. I have found over the years that most shortages are the result of someone stepping on the market process at some point. Sometimes this is actually done in order to force the commodity into your second category: Control by a centralized authority. There is little power in abundance.
Your fantasy that turning a commodity over to overlords to "distribute" will result in something being fairly distributed to those best able to use it does not stand up to history. In the real world, bribes, political influence, and irrational selection end up doing most of the job.