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From: Benoit Hoessen <b.hoessen_at_...6...>

Date: Mon, 22 Mar 2010 08:23:33 +0100

Date: Mon, 22 Mar 2010 08:23:33 +0100

Joachim wrote: >Thorsten Winterer wrote: >> >> (By the way, if I read it correctly, then Benoit's program has an >> additional constraint on the maximum stack height, namely that >> Height =< integer(ceiling(NumBoxes/NumStacks)). This makes the problem harder!) > >Yes, I'm a bit puzzled by that, maybe Benoit can explain. >It was not in the problem statement, maybe it is meant as >a heuristic in his program? In the program I made, to represent the constraint "the height of the stacks have a maximum height of H", I create fake boxes in order to completely fill the stacks. The additional constraint was set to minimize the number of fake boxes. This leads to minimize the total number of boxes and also minimize the total number of permutations for a given number of stacks. But, with that extra constraint, solutions may not be optimum e.g. if the boxes are the following: 12 boxes of dimension 4,4 and 1 box of dimension 5,3 then my solution won't give two stacks (the first filled by the 4x4 boxes and the second with only the 5x3 box) but 13 stacks of height 1. Also, solutions may not be correct with the initial problem e.g. 13 identical boxes will produce a solution using 1 stack. BenoîtReceived on Mon Mar 22 2010 - 07:23:40 CET

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