This THE reason why wal-mart, and in extention amazon, became that profitable and big. wal-mart tracked AND managed inventories to almost perfection. and amazon hired wal-mart supply chain experts pretty early on. you can the effects now. amazon is much more than just its website.
It can, not easily but most of the management needed by said corner store can be automated using SaaS. This approach combined with the app AND the point-of-sales data you can provide to smaller stores by doing so offer benefits for everyone. And the overhead won't be that big for the SaaS start-up as soon as economies of scale kick in IMO.