Packing problem when will a box fit in another box?

What the…?

Calculate the total volume of the biggest boxes, and calculate the volume that the smaller boxes contain, then find the optimum positions for each box to be in to pack them as effeciently as possible? and, it’s L x W x H

Or get some tetris whiz and just throw the boxes at him, it would be way easier.

its not that i am packing and moving….its like i want to find an answer for this mathematical question/puzzle

Not really a math question without the dimensions provided.

i need a generic algo Big Box Volume = (LxBxH), if I am packing another box in it say of (X,Y,Z) dimensions when would it fit in ?
@XOIIO i bet you can’t solve it

@ashek1 I could if I was given some dimentions to work with, otherwise, follow my first answer by calculating the volume.

The smaller box needs to be about a ½” smaller (all around) to fit properly into the larger box. What are you moving that needs double boxing?

Each of the boxes lengths widths and heights must be the thickness of the box smaller than the one on the outside.

What class is this homework for? Are nesting the boxes? Or is it just a bunch of random boxes all being fit into one big box?

Flatten out the little boxes and then lay them in the biggest box. As it get pretty full step on the ones on the top till they all fit.
Otherwise I agree with @talljasperman You have to consider the thickness of the boxes. I would measure the inside of each box and then you would know what size box would fit in it. Then you measure the outside of the next box, that is fitting inside.
Let’s say the first box is 16 inches in all directions on the inside than a box that is maybe 15 and a half inches on the outside will fit fine, but the inside of the box isn’t going to be 15 and a half. Maybe its 15 and a quarter inside. So the next box also has to be 15 inches to fit inside. And so on. So you are looking for thickness and volume.
Of course I’m just guessing. I may be wrong. But @tallijasperman makes sense to me.

If the smaller boxes are cuboid, rotating them inside the larger box isn’t going to make a lick of difference. Sheesh.

There is no efficient method for doing this. This article talks about the complexity of solving the problem when all the cubes are the same size. I would start out by considering the one dimensional case and see how far you can get.

@LostInParadise perhaps there could be a way check when a box would fit into another..

@zenvelo bunch of random boxes

@Pandora @talljasperman the dimensions here are inside dimensions…bigger worry is a kind of check that like 1) v<V and Space diagonal comparison , need that logic.

I think i have the solution two ways
1) Space diagonal of box (to be fit in) should be less that space diagonal of Bigger box, d<D

Another method a bit complex is to arrange dimensions in Decreasing Order and so that (L>B>H) and (x>y>z) box will only fit when x<L,y<B,z<H.

Can some maths genius verify this ?..or suggest some math forum where i can get this verified.
I am pretty sure it is the solution

Ask your teacher at your next class.

@Tropical_Willie its not a kids homework its a real business scenario have you ever thought how FedEx or UPS minimize the number of boxes to cut costs, dont reply anything just for the sake of it. FYI these kinds of problems are known as NP hard if you know what that means.

(oops. I wrote my answer thinking you meant the smaller boxes were cube shaped, but different sizes.. I see that, looking up the English word ‘cuboid’ can mean that they can have rectangular sides. ooops… sorry. In that case, turning them on their sides could make a difference in fitting the boxes.)

Again, what would be packed in them? Double boxing is not a common occurrence by either
FedEx or UPS.

Now then, several of the things I sell on ebay arrive double boxed from the China manufacturers. The only reason those items are double boxed is due to China’s poorly constructed corrugated cardboard.

When I send things via UPS or Fedex, they use Styrofoam, not a double box, to keep the weight down.

@ashek1 If you would have offered more details in your question, you’d get more reliable answers from the start. The way in which you worded this makes it appear as a math problem.

Again, I stand by my answer above (as I have a double boxed item in the room I type from. The inner box needs to be ½” less than the box it’s going into. That allows for less than ¼” of room between the layers.

@SpatzieLover i accept my mistake..but this is a real math problem. i know what you want to tell me but that is so obvious.

Yes, it is obvious: ½” smaller. What I am asking you is what else is it that you want to know? That is the measurement used to double box. Contact a box seller and they will tell you the same thing.

Is it that you want to use boxes where one (the outer) is sturdier, and one is paperboard or thinner corrugated?

You aren’t giving enough details. If it’s math you want, again, that isn’t how the box sellers do this. Why? It isn’t cost effective. They sell certain size boxes. It’s more cost effective for you and for them to use the stock they sell regularly. If you do a custom order, there will be a custom order charge.

ok..to give you an idea..these standards size boxes have some dimensions…and i want to fit same smaller boxes in one of those big box, since my customer is say is a medical store. now before doing that i want to calculate when a smaller box wont fit the bigger one etc…