[math-fun] length + width + height ??
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? -- 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? I guess we could start with all items being the exact same shape (same L, same W, same H) and packing them into a large cube. Then consider 2 types of items, with different L's, W's and H's, and then vary the percentage of the 2 types of items & see what happens to the packing density. Etc. -- A related backwards problem might be that of taking a large standard cube & cutting it into smaller pieces of different L's, W's and H's. If we made "random" cuts in all three dimensions, what are the statistics of the different shapes that fall out? These shapes obviously pack perfectly.
On 3/4/2012 11:09 AM, Henry Baker 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?
Mathematically, this would be the L1 distance between opposite corners of the box in R^3 with axes parallel to the box edges. Letting d be the standard L2 distance, we have 1 <= m/d <= sqrt(3), so m is a rough estimate of the box diagonal length. It also imposes an upper bound on box volume, with v <= (m/3)^3.
On 3/4/2012 11:09 AM, Henry Baker 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? Also, it is a simple measure that involves only addition, and applies easily to most packages.
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?
--
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?
[...]
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
participants (3)
-
David Wilson -
Henry Baker -
Robert Munafo