Cutting stock optimization

[Desiv5-disabled]

Hello everybody,

I would need an example of how to make a cutting stock optimization in Mathcad... should be only 1D (length cut optimization). Could somebody give me a hint?
Thank you in advance!

[Desiv5-disabled]

... hmm, the topic seems to be not very popular, or maybe too complex...

[ptc-1368288]

On 4/20/2010 7:52:42 AM, Desiv5 wrote:
>... hmm, the topic seems to be
>not very popular, or maybe too
>complex...
_______________________________

To me, cutting stock is cutting the plank,
just cut it to length ... in series.
I know a man who lost his job at the bank,
he was making money for them "cutting stock".
Now he makes their money at home, night shift, no Mathcad.

jmG

[LouP]

A lack of response is not surprising, since you have given us almost no information to work on.

If you would like some help, you will need to define much more precisely the problem you are trying to solve. You have given neither a mathematical decription of your problem and the optimization you would like solved (absolutely essential) nor an attempt at a mathcad worksheet (even better).

The more you provide up front, the less effort required of collab contributors to do, and the more likely someone will spend some time on your problem. Posting whatever you can do in a mathcad sheet (version 11 will have the widest audience) is a good place to start. Specific data always helps.

Peruse some of the other threads in the forum and you will get an idea of how to get good responses.

Lou

[Desiv5-disabled]

Oh, sorry, I will give now more detailed informations about what I need... (I mistakenly believed that it would be a well known problem)...
So, I would need to cut a number of elements of defined length from available bars of standard length (please see attached Mathcad file for numerical data). I want to know how to calculate the "arrangement" (combination) of the lengths, so that I will have at the end the least waste possible.
I hope I could define now a little bit better my question.

Thanks in advance for your support!

[LouP]

Well, it is a well known problem (but doesn't automatically register to some of us :-). I googled "cutting problem" and got hits for wiki and NIST among others, which may give some good quality info. Some of the links may help define the algorithm (seems to be a linear progr. prob.) in specific enough steps so that the coding into a mathcad program is relatively straightforward.

This is not an area I know well, so I'll leave it to more expert collabs, who may have already done this (or something similar).

Lou

[PhilipOakley]

With modern computers with large memory sizes and
high speeds it can be as simple as a complete
search. i.e. just try every combination - let the
computer do the hard work!


Philip Oakley

[RichardJ]

As Lou says, the math is well documented on the web. It would be a lot of work to code it in Mathcad though, so unless you get lucky and find that someone that reads these forums has already done this and is willing to share the worksheet, you will have to give it a go yourself.

Unfortunately, if you were going to be lucky it would probably already have happened.

Richard

[Ninetrees]

It is a minimizing problem in linear programming. If x[j are the # of sheets for pattern j, you want to minimize the sum(x[j) where sum(a[i,j * x[j) = b[i, subject to the constraint that x[j >= 0.

I imagine that your LP class is showing you how to set up the matrices so that you can solve A*x=b. This would give you a non-integer solution, though, so you must apply some thought to the solution to arrive at the actual minimum, and then convince yourself that it actually /is/ the minimum. I think that you will find the Wiki "Cutting stock problem" a useful place to begin.

Rich
http://www.downeastengineering.com/

[ptc-1368288]

Thanks Rich for the Wiki.

The best for "cutting stock" are the cabinet makers. They all do like I did at the time I had this hobby, they build it first in mind, no paper, no pencils. Not enough cut off to make an omelette. But it also depends the length of the planks. The best length is 7 ft, only very few 8 ft. In that Wiki paper mill example, experienced operators wouldn't waste anything ... no program, no computer. What their computer would do is simply recall the client # and plug in the cutting process if this last one is automated.

What kind of industry is that "cutting stock" about ?


Jean