Best way to arrange products for shipping?

[wajed]

I want to ship 5 products from the USA to my country.

I am trying to calculate the price, but I think it depends on the arrangement, so how do I calculate it? I can't simply add every corresponding dimension to the others, so how do I do it?

Here are the dimensions:-
16.35 x 10.8 x 1.46
11.1 x 8 x 4.8
3.9 x 2.7 x 0.4
3.9 x 2.7 x 0.4
8.7 x 2.9 x 18.5



I don't have products, I want someone to ship them for me, so I can't simply hold them and try to arrange them as best as possible. I'm asking for a mathematical solution to my problem

 

[berkeman]

I want to ship 5 products from the USA to my country.

I am trying to calculate the price, but I think it depends on the arrangement, so how do I calculate it? I can't simply add every corresponding dimension to the others, so how do I do it?

Here are the dimensions:-
16.35 x 10.8 x 1.46
11.1 x 8 x 4.8
3.9 x 2.7 x 0.4
3.9 x 2.7 x 0.4
8.7 x 2.9 x 18.5



I don't have products, I want someone to ship them for me, so I can't simply hold them and try to arrange them as best as possible. I'm asking for a mathematical solution to my problem

What are the units for those dimensions? Meters or cm?

Do any of the boxes have to be kept with their top's up? Or can all of them be put into any orientation? Can any box go on top of any other box?

Can you list the price schedule that will be used that shows the different charges for different shapes or volumes?

 

[wajed]

The unit is inches.

The boxes can be in any orientation and at any place (any box can top of any other.)

It's an online application that calculates the price. So, I only need to know the final dimensions and it will (internally) calculate the price and show it to me.

 

[berkeman]

The unit is inches.

The boxes can be in any orientation and at any place (any box can top of any other.)

It's an online application that calculates the price. So, I only need to know the final dimensions and it will (internally) calculate the price and show it to me.

If it were me, I'd probably just make the 5 boxes up out of folded paper, to help me get some intuition. Is that an option?

 

[wajed]

lol :D It is. But maybe it's better to do it accurately (mathematically.)

I'll try to make a program the does all the possible calculations and give me the least volume.

 

[yuiop]

lol :D It is. But maybe it's better to do it accurately (mathematically.)

I'll try to make a program the does all the possible calculations and give me the least volume.

I am pretty sure that will not be a trivial task. It will probably be easier to get a 3D program and model the boxes, manipulating them in a virtual environment. (I think Google has a free 3D program as part of the Google Earth project).

 

[yuiop]

From a quick sketch I get the smallest packing volume as 9.16*10.8*18.5 = 1830.168 cubic inches.

I don't think you will be able to do better than that, if the package has to be basically rectangular.

 

[wajed]

My head...

I tried to make the program, the result was weird as expected, lol, I got

35.25 * 27.1 * 7.1 =(approx) 6744

I entered your dimensions, and the price is OK! Thank you :)

By the way, just as a first step to make sure I'm even beginning right, how many possibilities/calculations are there? 16?

EDIT: my calculation will make me pay the double. I don't want it to be right!

EDIT2: if you used visualization software, can you give me a picture of the final result? If there is a pic (and you still have it,) I want to show it to my friend so that she puts the stuff the same way you put them.

EDIT3: I think it is not working because I tried every combination of adding the three dimensions.

 

[yuiop]

EDIT2: if you used visualization software, can you give me a picture of the final result? If there is a pic (and you still have it,) I want to show it to my friend so that she puts the stuff the same way you put them.

Here you go (see attachment).

I have colour coded the boxes as per this list (in the same order as your original list):

16.35 x 10.8 x 1.46 (Red)
11.1 x 8 x 4.8 (Blue)
3.9 x 2.7 x 0.4 (Black)
3.9 x 2.7 x 0.4 (Black)
8.7 x 2.9 x 18.5 (Green)

Note that you can easily change the order of the tall red, blue and green boxes, without changing the overall dimensions of the outer container if that works out more practical (to prevent bending for example). The black boxes can also be put in a number of positions (for example on top of the blue box) without any change in total volume.

 

[yuiop]

By the way, just as a first step to make sure I'm even beginning right, how many possibilities/calculations are there? 16?

It is actually a bit larger than that.

Each box can be rotated in 2*2*2 = 8 ways (not counting 180 degree turns which are duplicates).

There are 5 boxes so there are 8^5 = 32768 different ways of orientating the boxes with respect to each other.

Ignoring the 2 smaller boxes (which can placed in gaps), there 6 way of ordering the 3 larger boxes so the total permutations is 32768*6 = 196608.

Some of these arrangements amount to a simple rotation of the entire container package so they do not count. There are 4*4*4 = 64 ways of orientating a rectangular box (including 180 degree duplicates) so we can divide the number of permutations by 64 to get 196608/64 = 3072.

There are other factors, but that I think is reasonable ball park figure.

 

[wajed]

Thank you for the picture, it seems pretty obvious how to arrange the boxes, I just lack the imagination obviously!

And thanks for correcting and elaborating on the number of permutations.