An implementation of the 3D bin packing/knapsack problem (aka creating parcels by putting items into boxes)

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2.0 2016-05-30 20:09 UTC


An implementation of the 3D bin packing/knapsack problem i.e. given a list of items, how many boxes do you need to fit them all in.

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

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Wikipedia says this is NP-hard, and there is no way to always achieve an optimum solution without running through every single permutation. But that's OK because this implementation is designed to simulate a naive human approach to the problem rather than search for the "perfect" solution.

This is for 2 reasons:

  1. It's quicker
  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


If you use Composer, just add dvdoug/boxpacker to your project's composer.json file:

        "require": {
            "dvdoug/boxpacker": "^2.0"

Otherwise, the library is PSR-4 compliant, so will work with the autoloader of your choice.


BoxPacker is designed to integrate as seamlessly as possible into your existing systems. To use the library, you will need to implement the BoxPacker\Item interface on your item/product objects and BoxPacker\Box on the objects you use to to represent a box. These interfaces are quite minimal, but provide a standardised way for the packing process to obtain the dimensional information it needs in order to work.

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 Packer();
  $packer->addBox(new TestBox('Le petite box', 300, 300, 10, 10, 296, 296, 8, 1000));
  $packer->addBox(new TestBox('Le grande box', 3000, 3000, 100, 100, 2960, 2960, 80, 10000));
  $packer->addItem(new TestItem('Item 1', 250, 250, 2, 200));
  $packer->addItem(new TestItem('Item 2', 250, 250, 2, 200));
  $packer->addItem(new TestItem('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 = $packedBox->getBox(); // your own box object, in this case TestBox
    echo("This box is a {$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 $item) { // your own item object, in this case TestItem
      echo($item->getDescription() . PHP_EOL);


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

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

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

BoxPacker is designed to run calculations as efficiently as possible, the 4500+ tests in the test suite run in 11.9 seconds in the Ubuntu VM on my workstation, giving a rate of approx ≈385 solutions/second which should be more than sufficient for most e-commerce stores :) If you do wish to benchmark the library to evaluate performance in your own scenarios, please disable Xdebug when doing so - in my experience the unit tests take 4.5x longer (11.9sec->54 sec) when Xdebug is loaded.


  • PHP version 5.4 or higher (including PHP7 and HHVM)


BoxPacker is MIT-licensed.