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Size and construction of the specific shipping container under test [5] Grade and flute structure of corrugated fiberboard; moisture content of the corrugated board (based on relative humidity) [6] Orientation of the box during the test; Inner supports, if used during testing (wood, corrugated board, cushioning) Contents (when box is tested ...
Packing identical rectangles in a rectangle: The problem of packing multiple instances of a single rectangle of size (l,w), allowing for 90° rotation, in a bigger rectangle of size (L,W) has some applications such as loading of boxes on pallets and, specifically, woodpulp stowage. For example, it is possible to pack 147 rectangles of size (137 ...
Bin-packing with fragmentation or fragmentable object bin-packing is a variant of the bin packing problem in which it is allowed to break items into parts and put each part separately on a different bin. Breaking items into parts may allow for improving the overall performance, for example, minimizing the number of total bin.
Dimensional weight favors shippers of dense objects and penalizes those who ship lightweight boxes. A box of unpopped corn kernels will likely be charged by gross weight; a box of popcorn will probably be charged by its dimensional weight. This is because the large box of popcorn takes up a lot of space but does not fill up a vehicle's capacity ...
Best-fit is an online algorithm for bin packing. Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins of fixed capacity, such that the sum of sizes of items in each bin is at most the capacity. Ideally, we would like to use as few bins as possible, but minimizing the number of bins is an ...
In the optimal packing, the weight of each bin is at most 17/12; In the First-Fit packing, the average weight of each bin is at least 5/6 = 10/12. Therefore, asymptotically, the number of bins in the FF packing must be at most 17/10 * OPT. For claim 1, it is sufficient to prove that, for any set B with sum at most 1, bonus(B) is at most 5/12 ...