4D Packer Idea Using Cloudstek's LAFF Packer - splits items into increasingly smaller chunks until everything fits into boxes (based on dimensions and weight)

pack_items.php

<?php
//Uses: https://github.com/Cloudstek/php-laff
//THE doc: 'https://www.parkbeachsystems.com/images/usps/An_Efficient_Algorithm_for_3D_Rectangular_Box_Packing.pdf'

echo '<pre>';//readability

//DATA: array of defined boxes for shipping -outer and inner dimensions plus weight:
$boxes = array(
    array( 'ol' => 8.125,   'ow' => 8.125,  'oh' => 4.125,  'il' => 8,      'iw' => 8,      'ih' => 4,      'max_weight' => 20 ),
    array( 'ol' => 12.5,    'ow' => 9.875,  'oh' => 3.75,   'il' => 11.25,  'iw' => 9.75,   'ih' => 3.625,  'max_weight' => 10 ),
    array( 'ol' => 14.25,   'ow' => 9.375,  'oh' => 9.5,    'il' => 14.125, 'iw' => 9.25,   'ih' => 9.375,  'max_weight' => 30 ),
    array( 'ol' => 15.062,  'ow' => 11.25,  'oh' => 14.437, 'il' => 14.937, 'iw' => 11.125, 'ih' => 14.312, 'max_weight' => 60 ),
    array( 'ol' => 14.687,  'ow' => 12.625, 'oh' => 13.625, 'il' => 14.562, 'iw' => 12.5,   'ih' => 13.5,   'max_weight' => 40 ),
    array( 'ol' => 20.125,  'ow' => 11.25,  'oh' => 14.437, 'il' => 20,     'iw' => 11.125, 'ih' => 14.312, 'max_weight' => 60 ),
    array( 'ol' => 11.125,  'ow' => 9.125,  'oh' => 6.125,  'il' => 11,     'iw' => 9,      'ih' => 6,      'max_weight' => 20 ),
    array( 'ol' => 9.75,    'ow' => 3.75,   'oh' => 1.375,  'il' => 9.625,  'iw' => 3.625,  'ih' => 1.125,  'max_weight' => 1 ),
    array( 'ol' => 10.875,  'ow' => 4.875,  'oh' => 1.375,  'il' => 10.75,  'iw' => 4.75,   'ih' => 1.125,  'max_weight' => 1 ),
    array( 'ol' => 11,      'ow' => 7.25,   'oh' => 2.125,  'il' => 10.875, 'iw' => 7.25,   'ih' => 2,      'max_weight' => 2 ),
    array( 'ol' => 11,      'ow' => 9.75,   'oh' => 1.375,  'il' => 10.875, 'iw' => 9.625,  'ih' => 1.125,  'max_weight' => 2 ),
    array( 'ol' => 11,      'ow' => 7.25,   'oh' => 2.25,   'il' => 10.875, 'iw' => 7.125,  'ih' => 2.125,  'max_weight' => 4 ),
    array( 'ol' => 11,      'ow' => 9.75,   'oh' => 2.25,   'il' => 10.875, 'iw' => 9.625,  'ih' => 2.125,  'max_weight' => 4 ),
    array( 'ol' => 15.125,  'ow' => 11,     'oh' => 2.25,   'il' => 15,     'iw' => 10.875, 'ih' => 2.125,  'max_weight' => 6 ),
    array( 'ol' => 18.875,  'ow' => 1,      'oh' => 2.25,   'il' => 18.75,  'iw' => 10.875, 'ih' => 2.125,  'max_weight' => 6 )
);

//DATA: array of our items (products)
$items = array(
    array(
    	'name' => 'Product One',
        'length' => 12.5,
        'width'  => 16,
        'height' => 3,
        'weight' => 5
    ),
    array(
    	'name' => 'Product Two',
        'length' => 10,
        'width'  => 10,
        'height' => 5,
        'weight' => 7
    ),
    array(
    	'name' => 'Product Three',
        'length' => 9,
        'width'  => 11,
        'height' => 2,
        'weight' => 2
    ),
    array(
    	'name' => 'Product Four',
        'length' => 8,
        'width'  => 11,
        'height' => 1,
        'weight' => 4
    ),array(
    	'name' => 'Product Five',
        'length' => 4,
        'width'  => 4,
        'height' => 1,
        'weight' => 1
    ),
    array(
    	'name' => 'Product Six',
        'length' => 8,
        'width'  => 11,
        'height' => 6,
        'weight' => 2
    ),array(
    	'name' => 'Product Seven',
        'length' => 9,
        'width'  => 10,
        'height' => 4,
        'weight' => 3
    )
);

//required packer stuff
require_once( 'packer.php' );
$laff = new \Cloudstek\PhpLaff\Packer();

$done = FALSE;//our continue: yes | no FLAG
$chunk_size = count( $items );//first try to fit all items into a box
$divisor = 1;//this will be our incremental divisor if we need to split items into multiple boxes
$selected_boxes = array();//this will hold all of the boxes we will need when routine is done
while ( $done === FALSE ) {//try until done
    $items_temp = array_chunk( $items, $chunk_size );//split the items array into variable sizes (chunks)
    $results = pack_until_done( $laff, $items_temp );//hit our function below
    foreach ( $results as $result ) {
        $chosen_box_index = NULL;
        foreach ( $boxes as $k => $box ) {
            //length of requested box doesn't fit into width or length of our available boxes
            if ( $result['size']['length'] > $box['il'] && $result['size']['length'] > $box['iw'] )
                continue;
            //width of requested box doesn't fit into width or length of our available boxes
            if ( $result['size']['width'] > $box['iw'] && $result['size']['width'] > $box['il'] )
                continue;
            //same as above but height
            if ( $result['size']['height'] > $box['ih'] )
                continue;
            //same as above but weight
            if ( $result['weight'] > $box['max_weight'] )
                continue;
            //if we've made it this far we have a contender - figure cubic volume
            $vol = $box['il'] * $box['iw'] * $box['ih'];
            if ( $chosen_box_index ) {//we've alreay found a suitable box
                $prev_vol = $boxes[$chosen_box_index]['il'] * $boxes[$chosen_box_index]['iw'] * $boxes[$chosen_box_index]['ih'];//cubic vol of rpeviously selected suitable box
                if ( $vol < $prev_vol ) {//current suitable box is smaller than previous - save it
                    $chosen_box_index = $k;
                }
            } else {//save the index of suitable box
                $chosen_box_index = $k;
            }
        }
        if ( $chosen_box_index ) {//we found a box for the given set of items - save it in our array and set done flag to true
            $done = TRUE;
            $selected_boxes[] = array( 'box' => $boxes[$chosen_box_index], 'items' => $result['items'], 'total_weight' => $result['weight'] );
        } else {
            $done = FALSE;//no boxes found, break out of loop and try again
            break;
        }
    }
    if ( $done === FALSE ) {//continuing from the break - do the maths to chunk into smaller groups of items and run again
		$divisor++;
		$chunk_size = floor( $chunk_size / $divisor );
		if ( $chunk_size === 1 ) {//we've tried everything and hit the smallest chunk size (1 item per box) - you might have products that are too big or heavy to fit into ANY defined boxes
			$done = TRUE;
			$no_boxes_found = TRUE;//may not need this...could become useful, however
		}
    }
}

if ( selected_boxes ) {
	var_dump( $selected_boxes );
} else {
	var_dump( $no_boxes_found );
}

echo '</pre>';//end readability

function pack_until_done( $laff, $sets_of_items ) {//function accepts a packer object and arrays of items
    $total_sets = count( $sets_of_items );//how many sets are we processing?
    $need_boxes = array();//storage for required box size per set
    for ( $i = 0; $i < $total_sets; $i++ ) {//process all sets of items
        $laff->pack( $sets_of_items[$i] );//run Gürbüz's routine
        $items_count = count( $sets_of_items[$i] );//how many items in current set?
        //init vars for names and weight
        $item_names = array();
        $items_weight = 0;
        for ( $j = 0; $j < $items_count; $j++ ) {//loop through individ items to get names and total weight
        	$item_names[$j] = $sets_of_items[$i][$j]['name'];
        	$items_weight = $sets_of_items[$i][$j]['weight'] + $items_weight;
        }
        $need_boxes[$i] = array( 'size' => $laff->get_container_dimensions(), 'weight' => $items_weight, 'items' => $item_names );//store box dimensions, weight, and items
    }
    return $need_boxes;//return the data
}
?>