Is this one huge custom mixed stockpile? I see some items that look like ore scattered among the food. In that case that might be the cause.
No, it's just a food stockpile. The ore is just because some ore that was mined out hasn't been picked up yet.
They can fit. Could be you simply don't have enough containers. Food & booze can use both wooden barrels & rock pots. Trying queuing 30 of each and see if that helps.
I definitely have enough containers. My furniture stockpile is stuffed with barrels and bins and pots of every sort.
Maybe the stockpile isn't set to hold the max number of barrels.
Those stacks of 5 meat probably came from the trade caravan, which is why your food stockpile filled up quicker than the barrel-filling process could keep up. Barrel-filling is slow.
Check 'q' on the stockpile and 'R' to ensure it is set to the highest number of barrels (what Leonidas posted).
Check in 'p' to view stockpile settings for "reserved barrels". If that number is higher than the number of empty barrels in your furniture stockpile, then the problem is that all the empty barrels are being reserved for booze.
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Also, if your setting for the "mix food" order is "No mix" then the barrel-filling process will be slower (more barrels need to be moved to the stockpile because less food is being put in each one).
The stockpile is set to the max number of barrels. There are 9 reserved barrels for booze, and I have many more than that available. I do also have food mixing enabled.
Maybe you don't have enough free space to fit the barrels in the stockpile?
Those stacks of 5 meat probably came from the trade caravan, which is why your food stockpile filled up quicker than the barrel-filling process could keep up. Barrel-filling is slow.
I'm thinking this is likely what happened. I bought a lot of meat from caravans, and now there's no room for barrels. But also note that there are a lot of roasts in the stockpile, which were made by my own kitchen, and I would hope those would've been barreled. In an attempt to fix this, I've made another food stockpile for overflow. That stockpile is about half full of items outside of barrels and has no barrels whatsoever, despite being set for the maximum number of barrels. I have it set to give to the first stockpile, as the first is closer to where I want my food to be. Would that cause problems? It seems my dwarves just aren't prioritizing moving barrels to stockpiles when they have other things to move there. I haven't talked about it as much, but I have the same issue with bins in my finished goods stockpiles. I have quite a lot of empty bins in the furniture stockpile, but almost all of my finished goods are outside of bins.