is it possible to coordinate logistics with facebook apps

I would like to start a little app to coordinate grocery-shopping with my flatmates and near neighbours.

Users can use the app to bring each other groceries to save time. Users should be able to type in when they have time to bring groceries for others. On the other hand, Users should be able to type in, which groceries at which time they want to be brought from other users.

So does anybody know what the fasted way to build such a system? Could it be done with facebook apps or would you recommend another way?

Your help is much appreciated and would help me, me neighbours (and much more people, if the system spreads) to save a lot of time and hassle!

cheers, kampfkegel