All advanced civilisations have to ask themselves how to best optimize their supply lines. Handing over that duty to AI would give an efficient and most importantly an impartial delivery system. People are just numbers to the machines, they don't pick favourites... or do they? What's the loophole?
The delivery drones could allocate resources based on the number of citizens. One package per head. However, this may not be efficient. A child has higher caloric needs than an older person. Different jobs require varying levels of effort. Individuals have varying metabolic rates and so on... So the drones would profile individuals over time to best serve their caloric needs and optimize resource allocation. This would usher in an age of abundance. However enough isn't always enough. The system might be perfect but the people aren't. There's always people trying to get a bigger share of the pie.
So the question stands: why can't this autonomous world hunger-solving system not work? What's the flaw? How do you cheat the super smart hive-minded pizza delivery droids to get seconds? (Not just pizza. It's a figure of speech.)
EDIT: The AI is tasked with "feed every human being" and is left to its own devices. It will basically take over the entire food industry all the way from producing to processing and delivering. "Drone" in this case refers to all droids or robots handling the work and not just the UAVs we are used to. (Friendly reminder that this question is set in the future.)