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Thread: Combinatory optimization problem

  1. #1
    Apr 2010

    Combinatory optimization problem

    Dear experts,

    for a practical use in a warehouse I'm searching for a way to define this problem in an algorithm:

    We need to pick an article with a given amount $\displaystyle x$ where $\displaystyle x \in \mathbb N^+$.
    The article is distributed in several boxes in the warehouse. Each box contains the article in different amounts. So we have a limited amount of boxes $\displaystyle n$ with each box containing a quantity $\displaystyle y_n$ where $\displaystyle y_n \in \mathbb N^+$. We want to find the combination of boxes where the sum of the quantity of all selected boxes gets as close as possible to $\displaystyle x$ (but doesn't exceed $\displaystyle x$).

    Example for 7 boxes of this article:
    n & 1 & 2 & 3 & 4 & 5 & 6 & 7\\
    y_n & 15 & 17 & 8 & 20 & 19 & 20 & 18\\

    if $\displaystyle x=53$ then the ideal combination would be $\displaystyle y_1+y_4+y_7$ (15+20+18=53).
    if $\displaystyle x=30$ the best combination would be $\displaystyle y_3+y_4$ (8+20=28).

    It looks a little bit like a 0-1 knapsack problem to me but without the maximimizing of a value. Performance would certainly have to be considered. Can you help me to find an algorithm (I guess this problem is NP-hard)?

    Last edited by Skye; Apr 2nd 2010 at 10:49 PM.
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