包裹机箱型适配算法：多箱货物匹配柜型技术问询

之前我了解到这类问题属于装箱问题，目前尚无通用解法，因此重新梳理出更具针对性的问题，寻求解决方案：

包裹机的三种箱型参数 #

Array(
    "S" => Array(
        "width" => 380,
        "length" => 640,
        "height" => 90,
    ),
    "M" => Array(
        "width" => 380,
        "length" => 640,
        "height" => 190,
    ),
    "L" => Array(
        "width" => 380,
        "length" => 640,
        "height" => 390,
    ),
);

待装箱的货物盒参数 #

Array(
    "PRODUCT_1" => Array(
        "width" => $x1,
        "length" => $y1,
        "height" => $z1,
    ),
    "PRODUCT_2" => Array(
        "width" => $x2 ,
        "length" => $y2 ,
        "height" => $z2,
    ),
    ...
    "PRODUCT_N" => Array(
        "width" => $xN ,
        "length" => $yN ,
        "height" => $zN,
    ),
)

请问是否有方法判断这批货物盒能否放入上述某一种包裹机箱型？

内容的提问来源于stack exchange，提问作者Viacheslav Ravdin