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Minor spoilers below for the last module in the Jade Regent AP, The Empty Throne.
Today our brave party of adventurers heard of the food shortage issue from Isao. They immediately set out to resolve this situation, however we kind of run into a little problem. We were trying to figure out exactly how much rice are we talking about in that granary... One of my players came up with the random fact that a family of 4 in medieval Japan consumed 1 koku of rice over the course of a year, 1 koku being the equivalent of 150 kilograms (about 300 pounds) of rice. Kasai has a population of about 164000, so let's say 164000 / 4 = 41000 families, each eating up 150 kg of rice per year. That means a total of 6150000 kg of rice per year. We are assuming the bags in the granary each hold 50 kg of rice. Thus, we are talking about 123000 bags in total. Let's assume that the granary in fact only holds about half a year's worth of rice, we are still in the ballpark of about 60000 rice bags, each weighing 50 kg. This is the amount that should be stolen out of the granary in the dead of night, using carts supplied by Isao's buddies and distributed to the citizenry. Ummm, yeeeeaaah, right! This would need some serious logistics to pull off, really... Now we don't mean to criticize the module in any way, after all, we laughed so hard while figuring these numbers out and coming up with various solutions that it was much fun anyway. In the end the party decided to come up with an ingenious way of handling this, by opening a portal inside the granary, with the other end of the portal being somewhere far below the city in some natural cave, to store the "stolen" rice in. Since the portal has a limited duration they need to move this massive amount of rice quite quickly, so by clever application of the Reverse Gravity spell they mean to sort of suck all the rice from the ganary into the portal and be done with it. Meanwhile the druid is going to dig a tunnel down into the natural cave from an empty warehouse rented by Isao, so that the citizens of the city could get to the rice more or less undisturbed.
However we are curious about how other adventuring parties handled this particular problem? So if you have other, perhaps easier solutions, please do share. :-)

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In my group, the wizard and the cleric had to work together to figure it out (with the cleric intentionally getting himself eaten).
It involved spells like Getaway, Passwall and (for good measure) Explosive Runes after the fact. Then, it was just a matter of sticking a portable hole on the ground, and cantrip-sweeping all the rice into it.

Scharlata |

A portable hole has a volume of about (a litte more than) 10 cubic meters. Rice has a loose weight of 0.75 tons per 1 cubic meter. So, about 7.5 tons of rice would fit into a portable hole.
The 164,000 inhabitants of Kasai would make 41,000 "families" that will eat 0,150 tons of rice per year (or 0,075 tons of rice in half a year - a presumed storage quantity of rice in the granary).
So, there would be 3,075 tons of rice in the granary. If a portable hole could hold 7.5 tons of rice, this would make 410 trips to the granary and back to Isao's premises. Isao had to store 4,100 cubic meters of rice - about the dimension of a container of 16 meters times 16 meters times 16 meters, or a large family house or a captive balloon.

Gauldin |
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This is another area where I don't think the authors really thought this all through. My group hit the granary challenge last week, and took a different approach. I was already prepped with all the stats above (thanks, everyone!), so they knew in advance the volume of rice they'd be dealing with. I also told them that the granary had a double set of Typhoon Guards posted outside (the AP doesn't say anything about external guards, but there's no way the granary wouldn't be guarded against a city full of starving people).
After some noodling on how much they could move with the portable hole, how many D-Doors etc. they could muster, etc., one player asked "With all that rice, and the Jade Regent's troops consuming it, there must be people bringing rice in to replenish it, right?" A quick check on Google showed that rice has a 190 day growing cycle, so there could be two rice crops a year. That meant during the harvest season, there'd be a lot of rice flowing into the city. I rolled a d6 to see what month of the cycle they were currently in: month 6 - harvest!
Assuming the rice comes in at a constant rate through a 30-day harvest, that's ~100,000 kg per day. "How many wagons is that?" they ask. Back to Google, where I learn that a civil war wagon could carry ~3000 lbs. Close enough. That works out to roughly 65 wagons per day carrying rice to the granary. Since it would take ~16,850 kg of rice to feed everyone in Kasai for one day, that would mean ~11 wagon loads of rice. (At this point, our adventure was starting to feel like a series of story problems.)
So ... rather than storming the granary and trying to sneak many tons of rice out before the army arrived, they simply worked with Isao to "divert" 10-12 wagons to an "overflow" granary after they'd already passed the guards at the city gates. They paid the farmers for their rice (Paizo says wheat as a trade good is 1 cp/lb, so assuming the same price for rice, a full wagon would only cost 30 gp), and the farmers went on their way, suspecting nothing. In all likelihood, the people at the Imperial Granary won't even notice the shortfall for several days, giving the players plenty of time to move on to the Imperial Shrine and then storming the Palace.