Certain characters can be assigned task, but no progress is made. For instance, a certain character is assigned to alchemy, but no goods are produced.
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Did you set the craft queue for alchemy?
If you don't have enough of the required materials to make an item, it will stop all of the queue at that point. So in cooking if you have 1 bread then 20 meat soup queued up and have 500 meat and 500 veg but no grain, nothing will get made at all.
On the craft page the number to the right of the item is how many progress points are needed to make 1 of that item.
On the job assignment list, when you select the job, a number appears next to the person's name. That is how many progress points they make per turn.
Certain characters may have penalties for certain tasks (Inept reduces all crafting by 80%, Crude reduces tailor, smith and alch by 80%)
I don't know if this is the problem you are having but I had a glitch where the game thought 3 of my characters were still in a dungeon harvesting even though I had returned them to the mansion. I hit the forget location button while they still had materials to collect and the resources line stayed there not progressing.
I had to edit the save game and remove the duplicate hid from the ' "workers": [], ' line for the location in the save file.
I was having a similar problem, with both crafting as well as upgrading, and aevojoey's solution fixed it for me (thanks!). I went into the save file, searched for any instances of "workers":[] where I knew none of my characters were involved in that activity (there ended up being two instances of this), deleted the hid[ID#] from inside the brackets of the "workers":[], and changed the worker count to 0. When I re-loaded my save everything worked again.