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How to optimize shopping carts at the lowest prices?

I have a list of items that I want to buy. Items are offered at different stores and at different prices. The stores have individual shipping costs. I am looking for an optimal purchase strategy (and maintain its java library) to buy all items with a minimum total price.

Example:

  • Item1 is offered at Shop1 for $ 100, at Shop2 for $ 111.
  • Item2 is offered at Shop1 for $ 90, at Shop2 for $ 85.
  • Shipping cost Shop1: $ 10, if the total order is <$ 150; $ 0 otherwise
  • Shipping cost Shop2: $ 5 if total order <$ 50; $ 0 otherwise
  • If I buy Item1 and Item2 at Shop1, the total cost is $ 100 + $ 90 + $ 0 = $ 190.
  • If I buy Item1 and Item2 at Shop2, the total cost is $ 111 + $ 85 + $ 0 = $ 196.
  • If I buy Item1 in Shop1 and Item2 in Shop2, the total cost is $ 100 + $ 10 + $ 85 + $ 0 = 195.

I get a minimum price if I order Item1 and Item2 in Shop1: $ 190

Question

I need some tips on which algorithms can help me solve this kind of optimization problem for the number of items around 100 and the number of stores around 20.

I already looked at apache-math and its optimization package , but I have no idea which algorithm to look for.

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4 answers

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