Questions Tagged With packinghttp://www.or-exchange.com/tags/packing/?type=rssquestions tagged <span class="tag">packing</span>enWed, 30 Nov 2016 05:00:34 -0500Algorithms for box redesign in 3D-BPhttp://www.or-exchange.com/questions/14465/algorithms-for-box-redesign-in-3d-bp<p>Hi, dear experts,</p>
<p>Now I have some packing problems in E-commerce. Usually, some boxes (bins) of fixed size are given. Then the most suitable box (or a combination) is chosen to accommodate the items in order to minimize the material costs and logistic costs. This problem can be formulated as a standard 3D packing problem. Some heuristics are proposed, such as extreme points based method, the Guillotine algorithm, the maximal rectangles algorithm, etc.</p>
<p>However, if we are given different size of boxes (bins), we may have different packing solutions and different costs. The costs (material costs and logistic costs, the latter is proportional to the number of boxed used) can be reduced by redesigning the box size. But how to find a better size is really complex. 3D-BP is already NP-hard. The method I can only put forward is to constantly call our packing algorithms, for different box-combinations. However, it is really time-consuming.</p>
<p>Do you have some ideas to redesign the boxes to minimize the costs when packing given items? Any heuristics or mathmetical programming based methods are greatly appreciated. Thanks.</p>LinYuanWed, 30 Nov 2016 05:00:34 -0500http://www.or-exchange.com/questions/14465/algorithms-for-box-redesign-in-3d-bpbin-packingpackingmetaheuristics"Packing" Problem identificationhttp://www.or-exchange.com/questions/12544/packing-problem-identification<p>Hello I am trying to identify what could be the name of the following problem:</p>
<p>Let \(I\) be a set of items.</p>
<p>Let \(D\) be a set of defects.</p>
<p>Let \(l_i\) be the length of item \(i \in I\).</p>
<p>Let \(l_d\) be the length of defect \( d \in D\).</p>
<p>Let \(s_d\) be the start position of defect \( d \in D \)</p>
<p>Let \(c_{i,d}\) be a Boolean indicating if an item is compatible with a given defect.</p>
<p>Let L be the length of the material, that has defects, on which the items must be positioned. An item cannot be put on a position where it would intersect with an incompatible defect. The problem being to determine, if it exists a solution where no two items overlaps and where the compatibility with the defects is respected.</p>
<p>If I am considering that all lengths are integer, a possible formulation could be the following:</p>
<p>Let \( x_{i,j} \) be a binary variable indicating if the left of item \(i\) is positioned j units of measure away from the left of the start of the material. I'll consider that variable that would imply putting an item on an incompatible defects are already fixed to 0.</p>
<p>Then the constraints are.</p>
<p>\( \sum_{j \in [0,L]} x_{i,j} = 1, \forall i \in I \) </p>
<p>\( x_{i,j} + x_{i',j'} \leq 1, \forall i \in I, i' \in I, j \in [0,L], j' \in [j,j+l_i] \) </p>
<p>I have already tried to give a look to packing problems with defects, but could not really find something related to the 1 dimensional case, any pointers about what the name of this problem (or a similar problem) could be are welcome.</p>RenaudFri, 26 Jun 2015 03:00:59 -0400http://www.or-exchange.com/questions/12544/packing-problem-identificationpackingidentificationdefects