Efficiently feeding allies?

Are there any recommended methods of keeping allies fed? I have 6 allies now, one of which is parasitized (thankfully), but keeping a T-Rex, Carbuncle (mount), Fox Maid, and two NPCs fed feels basically impossible. I've got a container I use for only food and try to buy up good food from stores to help increase skills, but am not sure how to keep them from being starving 95% of the time when roaming the world map or entering a Nefia.

Does anyone have a method they find works well to hold a large amount of food on-hand?