What Is the Best Algorithm for Finding the Cheapest Supplier Combination?

[chriswaller]

I have a problem in which I have people ordering different goods from my website and I have a number of suppliers who provide these goods, but I need an algorithm to find the cheapest combination of supplies from each supplier. It would seem easiest to just see which company offers the product at the lowest price, but I need to take into account that it may be cheaper delivery if I order from as few people as possible, and also that not every supplier will offer every product.

Does anybody know a good algorithm for working this out or have any advice on the problem? Any help would be very much appreciated, no matter how small.

 

[Mark44]

I have a problem in which I have people ordering different goods from my website and I have a number of suppliers who provide these goods, but I need an algorithm to find the cheapest combination of supplies from each supplier. It would seem easiest to just see which company offers the product at the lowest price, but I need to take into account that it may be cheaper delivery if I order from as few people as possible, and also that not every supplier will offer every product.

Does anybody know a good algorithm for working this out or have any advice on the problem? Any help would be very much appreciated, no matter how small.

This type of problem is standard fare in Operations Research, and the particular area is called Linear Programming. In a typical problem, the goal is to maximize profit, taking into consideration a number of constraints, such as production costs, supply costs, availability of machinery, and so on.