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POOptimization – Rearranging items of a specific type?
 

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  1. POOptimization – Rearranging items of a specific type?
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    <p>Optimization – Rearranging items of a specific type? Here’s a little optimization problem for a personal project I’m working on: so imagine you have many boxes of an item, and within each box, you know that the items must be shipped to various locations. </p> <p>Example: </p> <blockquote> <p>Box 1: 1000 items, 500 to location A, 500 to location B.</p> <p>Box 2: 1000 items, 500 to location A, 500 to location B. </p> </blockquote> <p>I want to be able to rearrange the items such that I can ship as many full boxes as I can to one destination. For instance, in the example above, I would be able to rearrange the items such that new_box 1 has 1000 items to location A, and 1000 to location B.</p> <p>Now you can imagine that this perfect rearrangement case will not always occur. What if I had:</p> <blockquote> <p>Box 1: 1000 items, 500 to location A, 300 to location B, 200 to location C.</p> <p>Box 2: 1000 items, 500 to location A, 500 to location B.</p> </blockquote> <p>Then, I would want to (a) optimize the number of full boxes to one destination, &amp; (b) minimize the number of <em>different</em> locations in every other box. For instance, having 3 boxes each with 2 different destinations would be better than having 3 boxes each with 3 different destinations. The optimum rearrangement of the second example above would be:</p> <blockquote> <p>New_box_1: 1000 items, 1000 to location A.</p> <p>New_box_2: 1000 items, 800 to location B and 200 to location C.</p> </blockquote> <p>My question is: <strong>How would I handle this situation for arbitrary number of boxes and arbitrary number of destinations per box?</strong> For the sake of the problem, let’s start with assuming that each box has the same number of items.</p> <p>What I’m thinking right now is to take a greedy approach:</p> <ol> <li>Go down the line for each subsequent box and keep a running sum of the destinations and the number of items that will be shipped to it.</li> <li>If any of these sum to a value that is greater than the box capacity, place these items in their own box.</li> <li>Then, take the highest number of items to one destination that is remaining, call this “x”, take the value (box capacity – x), (call this “y”), and find the value of the number of items to one destination that is both ABOVE “y” and the closest to “y”.</li> <li>Then, place “x” items to the first destination and “y items to the second destination in another box, and repeat. </li> </ol> <p>Any other suggestions, or insights? Thanks so much.</p>
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    1. USRolando Isidoro
    1. USRyan Yu
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      1. USBytemain
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    1. COI swear at first I thought this was a P=NP joke/gag question. Turned out quite interesting.
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      1. POOptimization – Rearranging items of a specific type?
      1. USLayke
    2. COSounds like a variation on the knapsack problem....
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      1. POOptimization – Rearranging items of a specific type?
      1. USdchhetri
    3. COHmmm, what do you mean? There can be any initial distribution of destinations in a box, I think.
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      1. POOptimization – Rearranging items of a specific type?
      1. USRyan Yu
 

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