Let's assume that these services are motivated by profits, and that there is enough competition to ensure that the prices track carefully to the costs. Let's further assume (for the moment) that weight doesn't matter; that the real problem is merely fitting the packages into the container for shipping. Let f(L,W,H) be a function that approximates the cost of shipping, and we will price based on some "cost plus" model. What would be a decent function to use that would maximize the value that one could carry? Clearly, if the standard container is 20'x8'x8', we can completely fill it with 4'x4'x4' cubes. But if we can charge more (per unit volume) for non-cubical shapes, we could still maximize the shipping value of the container, even though the container still might have some empty spaces. So what would an "optimal" f(L,W,H) look like? I would guess that f() is symmetric in all of its arguments, but perhaps that isn't even obvious. f() would somehow charge more per unit volume, the "odder" the shape is, because I assume that the statistics of the types of objects would make it less and less likely to be able to pack the container completely full. Note that mere simplicity of computation isn't all that important if the shipping costs are high enough; one would quickly implement a more sophisticated pricing function if there was significantly more profit in it. So, given these constraints, is f(L,W,H)=C*(L+W+H) even close to optimal? At 11:48 AM 3/4/2012, Robert Munafo wrote:
I think it's a lot simpler than that.
They're trying to give a "volume discount" for customers with lage packages. To some extent, if the customer had to pay 8 times as much for something that has 8 times the volume (2x in each direction), they'd probably consider it overpriced.
There is also an intentional surcharge for oddly-shaped packages, for the packing reason you mentioned and for other reasons.
"length + width + height" fairly neatly encapsulates both of these objectives.
On Sun, Mar 4, 2012 at 11:09, Henry Baker <hbaker1@pipeline.com> wrote:
Some airlines & postal systems charge by the curious measure "length + width + height".
1. Is there a standard name for this measure?
2. What is the scientific/mathematical rationale for using this measure for charging?
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If there were such a mathematical rationale, I would think that it would somehow be based upon the statistics of packing many dissimilar boxes into a standard box -- e.g., a standard shipping container or a UPS truck.
What do we know about the statistics of packing various numbers of differently shaped boxes into a large cubical box?
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