Imagine this situation:
In a certain city are a number of suppliers and a number of customers. Each
customer demands a certain amount of several different products. Each
supplier has a certain amount of each of these products in stock. Trucks
with unlimited capacity transport multiple (different) products from only
one supplier to only one customer, but each trip costs the same lot of
money.
Now the question is:
How can the cheapest way be found to deliver all demanded products to the
customers?
I think that there should be some algorithm around solving this problem as it is a quiet standard one. But I have done some research and I am not able to find it. I think it is not a standard Transportation Problem, because more products are involved and costs are not defined per transferred product.
Any ideas or links will be very much appreciated!
Assuming I understand the question correctly (the wording is a bit vague in places), it can be modeled as an integer linear program. As far as "standard" problem types that might apply, I think you can formulate it as a one-dimensional cutting stock problem. What would be a piece of "stock material" now becomes a truck from a specific supplier to a specific customer. A "pattern" is now a possible load for a given truck (so much of this product, so much of that product, ...). Since the trucks have unlimited capacity, the limitation on what goes in a pattern is the lesser of how much of each product the supplier has and how much the customer wants. The "waste" for a pattern translates to the cost of dispatching the truck.
While it can be formulated that way, I would not recommend doing so.