[Patrick Flynn]

I think that a possible way to improve this process would be to split the stock of FIRST choice products into thirds or even more. Have the first third of teams be allowed into first choice at 10-am and then close at 11:50-am, the second set of items for the second third of teams would be open 12-1:50 and so on. After all the divisions of teams had received their allowed time, the store could open back up and everyone could pick over the left over items.
All the teams would initially have access to the same number of parts, and after the whole process you would still be allowed to chose an item that all of the teams from a different ordering block didn't want.