Given a list of items to buy on an e-commerce, generate the cheapest possible cart (which obviously includes all the items).
The items can be purchased from many sellers at different prices.
Sellers have a subset of your articles. (It's unlikely that a seller has all article you need.)
All the sellers have the same shipping cost and this is linear respect to the spending.
I know that this is an Integer Linear Programming problem, but I'm unable to express the shipping constraint in the canonical ILP form.
My Operations Research professor told me that this is a sub partition problem, but I don't know what is.
In an average use case there are about 100 articles to purchase.