The fundamental problem with minimum wage as presently imagined by the idiots is that it is price control rather than market intervention. This makes it market interference. Market interference by regulation is meaningless unless it is combined with a properly managed market with ample liquidity.
Without true planned and capitalized liquidity you have a discount market in which a portion of the population is not able to participate except as slaves which is obviously illegal. That means they do not work and instead are enslaved to a government handout and all the baggage associated with that.
Since it is obviously stupid it needs to be addressed. I have done that through the creation of the four hour standby job that provides a night's rest in a warm bed, a shower, laundry, breakfast and lunch in exchange for four hours of light work. This protocol is easily implemented using resources already available and its purpose is to make the idea of a minimum wage meaningful.
Thus worker can after lunch then take on a full eight hour shift if it becomes available and not disturb his options..