Optimizing a mail-order with discount and shipping costs

Artikel i vetenskaplig tidskrift, 2002

We address the problem of minimizing the total cost of a mail-order if a customer can choose among different companies. These companies may offer the items in his shopping list at different prices, and they add some charges or give discount, depending on the total value of ordered goods. While this optimization problem is hard in general, we show that it can be efficiently solved for some typical discount policies, either exactly or by invoking an approximation scheme for the Knapsack problem.