Looking for supplier price optimization algorithm

Question

I'm looking for an algorithm for the following problem:

I have a set of x distinct components and a set of y supplier for those components. I know the price p(x,y) for each component from each supplier. I also know the shipping cost s(y) for each supplier, which is obviously cheaper if you just buy from just a few suppliers. Not all suppliers have each component available. I want to buy all components once, but need to get the cheapest total price or at least a very closed small value.

The straight forward approach would be to try each combination, which could take some time if x and y get very large, although it could be parallelized. Any suggestions are appreciated.

For simplicity let's say x = 100, y = 1000.

Answer 1

Thanks for all the comments. They pointed me in the right direction, to formulate the problem like displayed below.

Minimize the sum of all items plus shipping costs:

p(0,0)*x00 + p(0,2)*x02 + p(1,2)*x12 + ... + ship(0)*y0 + ship(1)*y1 + ...

with x and y in [0,1], p(n,m) is the price of item n for supplier m and ship(m) is the shipping cost for supplier m

Subject to:

1. Retrieve each item exactly one time, like this:

p00 + p01 = 1
p12 + p13 + p15 = 1
p20 + p21 = 1
...

2. Shipping cost is taken into account if one item is bought from this supplier

y0 >= x00
y0 >= x10
y1 >= x01
...