#artatus verb
conjugation: 1st conjugation
voice: transitive

Definitions:

• compress, abridge;
• pack, limit, cramp;
• wedge in, fit/close firmly, tighten

An traditional (non-namespaced) implementation of the 3D bin packing problem i.e. given a list of items, how many boxes do you need to fit them all in.

This implimentation is inspired heavily by dvdoug's BoxPacker but is both implimented as a practial solution and in a non-namespaced manner.

Especially useful for e.g. e-commerce contexts when you need to know box size/weight to calculate shipping costs.

Wikipedia says this is NP-hard, and there is no way to always achieve an optimum solution without running through every single permutation, which is massively inefficent on time and CPU cycles, but that's OK because this implementation is designed to simulate a 'balanced naive' (a.k.a. human) approach to the problem (similar sized boxes are better) rather than search for the "perfect" solution.

This is for 2 reasons:

1. It's quite a bit quicker; and
2. It doesn't require the person actually packing the box to be given a 3D diagram explaining just how the items are supposed to fit.

• Pack largest (by volume) items first
• Pack vertically up the side of the box
• Pack side-by-side where item under consideration fits alongside the previous item
• Only very small overhangs are allowed (10%) to prevent items bending in transit
• The available width/height for each layer will therefore decrease as the stack of items gets taller
• If more than 1 box is needed to accommodate all of the items, then aim for boxes of roughly equal weight (e.g. 3 medium size/weight boxes are better than 1 small light box and 2 that are large and heavy)

• Items are assumed to be shipped flat (e.g. books, fragile items). The algorithm as implemented therefore considers simple 2D rotation of items when determining fit but will not try turning items on their side
• The algorithm does consider spatial constraints in all 3 dimensions, plus consideration of weight

just require 'lib/artatus.php'

Basic usage then looks something like the below: (although you'd probably want to do something more useful with the results than just output to the screen, and your dimensional data would hopefully come from a database!)

  /*
   * To figure out which boxes you need, and which items go into which box
   */
  $packer = new ArtatusPacker();
  $packer->addBox(new ArtatusBox('Le petite box', 300, 300, 10, 10, 296, 296, 8, 1000));
  $packer->addBox(new ArtatusBox('Le grande box', 3000, 3000, 100, 100, 2960, 2960, 80, 10000));
  $packer->addItem(new ArtatusItem('Item 1', 250, 250, 2, 200));
  $packer->addItem(new ArtatusItem('Item 2', 250, 250, 2, 200));
  $packer->addItem(new ArtatusItem('Item 3', 250, 250, 2, 200));
  $packedBoxes = $packer->pack();

  echo("These items fitted into " . count($packedBoxes) . " box(es)" . PHP_EOL);
  foreach ($packedBoxes as $packedBox) {
    $boxType = $packedBox->getBox(); // your own box object, in this case ArtatusBox
    echo("This box is a {$boxType->getReference()}, it is {$boxType->getOuterWidth()}mm wide, {$boxType->getOuterLength()}mm long and {$boxType->getOuterDepth()}mm high" . PHP_EOL);
    echo("The combined weight of this box and the items inside it is {$packedBox->getWeight()}g" . PHP_EOL);

    echo("The items in this box are:" . PHP_EOL);
    $itemsInTheBox = $packedBox->getItems();
    foreach ($itemsInTheBox as $item) { // your own item object, in this case ArtatusItem
      echo($item->getDescription() . PHP_EOL);
    }

    echo(PHP_EOL);
  }



  /*
   * To just see if a selection of items will fit into one specific box
   */
  $box = new ArtatusBox('Le box', 300, 300, 10, 10, 296, 296, 8, 1000);

  $items = new ArtatusItemList();
  $items->insert(new ArtatusItem('Item 1', 297, 296, 2, 200));
  $items->insert(new ArtatusItem('Item 2', 297, 296, 2, 500));
  $items->insert(new ArtatusItem('Item 3', 296, 296, 4, 290));

  $packer = new ArtatusPacker();
  $packedBox = $packer->packIntoBox($box, $items);
  /* $packedBox->getItems() contains the items that fit */

• PHP version 5.3 or higher

artatus is MIT-licensed.