Is there a site where I can put in a set of individual lego bricks (by part ID) and get an optimized list of stores to buy (to minimize shipping) I'm new to this site, so please forgive me if this is a duplicate. 

Background story
I got my 6 years old the Lego City Arctic largest set, and then realized he had previously had 2 other arctic sets, that sadly, he lost some parts for... 

I have sorted through all of his legos (yes, I do have a life, but this was rewarding on unbelievable and weird levels) and checked marked all the pieces he had. I narrowed it down to the few that he was missing and got their ID number. 

I Googled my way into http://www.wallofbricks.com/ and was able to find stores that sell all those pieces! 

Problem

The big problem as you might have guess is that it would cost more than re-buying that set again. The difference is not the individual piece cost of course, but the shipping. 

The issue stems from the obvious reason that not all stores have all pieces, so you just pay a lot in shipping...

Now, I'm sure that if I cross reference the online stores that sell all the parts, I'll be able to find some, that might not have the cheapest price, but have more than one piece in stock. 

Question 
This is a very interesting optimization problem to solve, and I was wondering if there is any website that lets you answer the give question: 

Given a list of missing pieces and quantities, and the original set cost - finds either the combination of stores such that the piece costs + the shipping is less than the original set, or suggest that buying the original set will be cheaper.
There are two pieces of software that lets you do this for Bricklink: Brickficiency and Brick Wizard. The latter seems updated more often, but I don't know if they produce different results.