## Cutting Foam Block:

### Cutting Foam Block:

Special Order Tapered Foam Cuts.

I have anywhere from 6-11 different dimensions to cut from 4' x 4'
foam blocks. 620 Board Foot (bd ft) is the maximum usable foam per
block. My qtys vary in size from 21-107 pcs, and I can calculate the
bd ft per piece. Each combination of cuts from a given block
represents a "wire set" that is manually set-up. The trick is to
minimize wire sets, elimimating as many labor hours as possible. I
want to get as close to 620 bd ft with each cut (wire set) without
going over. If I can allocate as much of the 620 bd ft as possible, I
have 3 different "default" sizes ( 36,18 & 8 bd ft) which can be sold
out of regular stock. IOW - If my first wire set only totals up to 612
bd ft, I can cut 1 pc of the default size of 8 bd ft.

What I need is an algorithm to produce the number of wire sets, and
runs per wire set of X number of pcs needed, without going over total
required qty per each piece, while cutting the least number of default
pieces as possible.

Do I need a math genius to figure this one out?

I don't even know step 1. I mean, do I start with the biggest qtys of
In theory, the first few cuts will have the greatest run qty,
descending with each wire set.

Thanks, Dave.

### Cutting Foam Block:

Hello Dave.
Is a board foot a measure of area or
volume? Are we assuming the initial blocks are
all 4X4X38.75 =620 cubic feet?
Might be an idea to take this to sci.math and
if they can come up with an algorithm then
It looks like a "Set Packaging Problem" to
me. These are often very hard to solve
optimally.
Cheers Mick.

### Cutting Foam Block:

Hi Mike,
question to sci.math and received a response from Clive. His questions
and my responses are at the bottom of this post.

My response to Clive from sci.math:

Hi Clive,

Thank you for your prompt reply and questions. I'll see if I can
make more sense out of my original question by answering yours:
1) Is this essentially a 2-dimensional problem? That is, are all the
cuts perpendicular to the two 4'x4' faces of a foam block?
No...we are cutting tapered sheets of (styro)foam insulation to match
the pitch of a roof, to be laid beneath the shingles.
2) What is the definition of a Board Foot?
A unit of cubic measure for material, equal to one foot square by one
inch thick, i.e. the VOLUME of that piece of material. A piece of
material with the dimensions 1" x 4' x 8' = 32 board feet.
3) How complex are the shapes that you are trying to produce?
- Can you say what these shapes are? Please see #1 answer.
- What is meant by "Tapered Foam Cuts"? Front face of sheet may be .5
" - Back face may be 2".
-
- How are the shapes defined? If you loook at the end product from the
side it will look like a triangle or tapered rectangle.
- Are any of the faces curved? No.
- What is the maximum number of faces that a shape might have? 6 -
Front, back, top, bottom & two sides.
4) Can you say more about what a wire set is? We cut the block of
foam with hot wires. A wire set is the setting for the wires to cut
one block, yielding X number of different angled sheets.
pictures of this product, these are a special order product that vary
in dinensions. Just think of a triangle with volume.
Thank you again,
Dave

### Cutting Foam Block:

Hello Dave.
It now appears that you want to get the optimal
number of specific trapezoidal or wedge shaped chunks
from a rectangular block. But you need to balance this
against the cost of resetting your wire rigs; so that a less
than optimal use of the original block may be the
best cost-wise. This is a truly monsterous problem!
But as the "Blue Bell" example from sci.math demonstrated
it is one well worth solving if you are in large scale production.
I recently spent over 100 hours trying to code "Set Covering
Problems" in VB. Your "Set Packaging Problem" looks
every bit as difficult! This is one for the professionals in
"Design Theory".
Good Luck. Mick.

### Cutting Foam Block:

Hi Mick,

"monstrous problem." Now I don't feel as stupid in that someone else
with smarts realizes that this is a tough one.

You are right about the "wedges" we are cutting, I wish I would have
thought of that word with my original question. It would have made it
easier for everyone that has helped me to visualize the end product.

The problem will be solved. I may need to resort to VBA and Excel (as
the professor suggested.) I can see having Excel run the numbers for
combinations of qtys that total per wire-set of 600-620 board feet, and
adding the a default (stock) piece whenever you get close to, but less
than the magic 620 brd ft. Then it could multiply the runs unitl you
reach the max qty for the lessor of the several pieces being cut in the
wire-set. Then I could move to the right in columns carrying over the
balance due per piece until all qtys of pieces are filled. Then
repeating the process for each wire-set. Regarding the \$\$
productivity, I would probably just need to assume that the least
number of wire-sets required = the most efficiency.

Well, thanks again and maybe we'll bump into each other again sometime.

Dave