Why not just eliminate the paper to begin with? It's obviously a bit tougher as you need to tackle both sides of the market at once, but not having to mail invoices means the benefit of faster payments for suppliers (maybe not a benefit to the restaurant however) and could enable just-in-time ordering from the restaurant.

It might even flip the invoicing on its head. When the restaurant orders, it creates a transaction. The supplier delivers and the restaurant completes the transaction, generating a payment. Now the restaurant can order only what it needs, faster, and the supplier receives its payment faster.