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Here is a proof that the asymptotic ratio is at most 2. If there is an FF bin with sum less than 1/2, then the size of all remaining items is more than 1/2, so the sum of all following bins is more than 1/2. Therefore, all FF bins except at most one have sum at least 1/2. All optimal bins have sum at most 1, so the sum of all sizes is at most OPT.
For each item from largest to smallest, find the first bin into which the item fits, if any. If such a bin is found, put the new item in it. Otherwise, open a new empty bin put the new item in it. In short: FFD orders the items by descending size, and then calls first-fit bin packing. An equivalent description of the FFD algorithm is as follows.
Isuzu Elf box truck. A box truck—also known as a box van, cube van, bob truck [1] or cube truck—is a chassis cab truck with an enclosed cuboid-shaped cargo area. [2] On most box trucks, the cabin is separate to the cargo area; however some box trucks have a door between the cabin and the cargo area, box trucks tend to be larger than cargo vans and smaller than tractor-trailers with movable ...
Reach truck handling stretch wrapped unit load Air cargo container of the AKH type on a trailer. The term unit load refers to the size of an assemblage into which a number of individual items are combined for ease of storage and handling, [1] for example a pallet load represents a unit load which can be moved easily with a pallet jack or forklift truck, or a container load represents a unit ...
In the maximum resource bin packing problem, [51] the goal is to maximize the number of bins used, such that, for some ordering of the bins, no item in a later bin fits in an earlier bin. In a dual problem, the number of bins is fixed, and the goal is to minimize the total number or the total size of items placed into the bins, such that no ...
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 ...