Three-Dimensional Bin Packing Problem - php algorithm

We are going to develop an web app for solve 3D BPP using PHP. Geven the boxes having special size(width W, length L, height H) and 80~200 boards having several size(width w(i), length l(i), height l(i), 0<i<=200), in order to optimise the space in the boxes, we need to arrange them as best as possible. INPUT VALUES 1. Size of boards {w(i), l(i), h(i), 0<i<=200}. We usually work with 4 hights (25, 18, 8 and 3 mm). 2. Size of box {L, W, 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 generally {L=2700mm, W= 620mm, H=150mm} 3. Max of package weight(the weight sum of box and boards in it). (usually, no more than 35 kg/ package) OUTPUT VALUES 1. Number of boxes and their SIZE. 2. Box number for each board (in which of the boxes will the board be placed). 3. Position of each board in the box (start numbering from the front, left, bottom) ADDITIONAL INFORMATION The density of the 18mm panel, 13 kg/m2 The density of the 25mm panel, 18 kg/m2 The density of the 8mm panel, 6 kg/m2 The density of the 3mm panel, 1 kg/m2 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, Position Array(x(i), y(i), z(i)) 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.