Stacking boards into boxes for delivery - php algorithm

We are a furniture manufacturer in Romania. We are developing an online platform for selling furniture. In order to deliver the furniture, we need to pack all the boards and fittings.

In order to optimise the space in the boxes, we need to arrange them as best as possible. This is why we need a stacking algorithm.

Basically, we need to generate the label for each board (with information regarding box and row in the box) before launching in the production.


1. List of boards [W x L x H] - H = board thickness. We usually work with 4 thicknesses (25, 18, 8 and 3 mm).

2. Max. package dimensions [L x W x H] - The boxes will be manufactured using a cardboard cnc cutter depending on the stacking solution for that order given by the algorithm. The max dimensions are [L=2700mm, W= 620mm, H=150mm]

3. Max. package weight. [usually, no more than 35 kg/ package]


1. Number of boxes and their dimensions.

2. Box number for each board (in which of the boxes will the board be placed).

3. Row number in the box(package) [start numbering from the bottom up]


The density of the 18mm panel, 13 kg/m3

The density of the 25mm panel, 18 kg/m3

The density of the 8mm panel, 6 kg/m3

The density of the 3mm panel, 1 kg/m3

The tolerance space in the box is aprox 4 mm on each side.

These variables will be defined at the beginning of the script or in a txt file so that the values can be changed in the future.

Also, the output file fill be a txt or the values can be inserted in a database table.

The final info:

Board ID, Box number, Row number in the box for each board

Box dimensions for each box.

In conclusion, the algorithm will process the list of boards and will determine the minimum number of boxes, the best dimension for each box, in which box every board will be placed as well as row number in the box.

Please see the file attached. It contains and example of boards list.

Taidot: Algoritmi, PHP

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