# Thread: Applied math problem - creating a cut list

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## Unanswered: Applied math problem - creating a cut list

I realize this gets into business logic, but a DB based solution might be best. Possibly some pre-calculated measurement tables.

Business problem: Creating a cut list for a window covering (blinds) system. It's preferably a fast calculation I could execute while the user awaits "order confirmation and pricing". A .5 second delay per order would be acceptable.

An order can have unlimited number of line items, but typically between 1 and 20 (number of windows in a single house).

(For this problem) the raw material is man-made, and therefore is always the same length for a particular pattern/color (take 12' for this example; we stock patterns in 9', 12', or 16' but it's always the same for a given pattern/color). I need to tell the cutters how to use the rawmaterial with minimal waste. Note: The saw blade takes 1/16th inch.

For each line item; I have pre-calculated the exact cut size and number of slats. Measurements are in inches at 1/8 (.125) inch increments. The length of raw material length we stock for this pattern is an easy link.

The goal is to average less than 6 inches waste per 12' piece of raw material.

Example order:

5 line items for pattern/color FAUX/white, stocked in 12' lengths.

Line 1: 34 slats at 35.125 inches.
Line 2: 36 slats at 36.875 inches.
Line 3: 50 slats at 42 inches.
Line 4: 55 slats at 70 inches.
Line 5: 52 slats at 30 inches.

The resulting cut-list-workorder would evaluate all lines together and tell them how many 12' slats to pull and how to cut them with minimal material waste.

My question:

I'm left wondering if a database style pre-populated answer list (or some other database based solution) might be a lot faster and simpler than some chess-style complex trial-and-error array based VB algorythm (that I haven't even begun to imagine how to write). If so; how would it look?

In addition; the cutters get something like \$10/hr so we can't make it too complex. I'd rather waste a little material and avoid undue confusion, but not much. With \$5+ million in this material per year, excess waste can really add up. Imagine the difference between 12% and 15% waste. It's an area worth investing in.

Sorry; I know it's not a simple question. Someone might find it interesting enough to solve, or at least provide hope for a DB solution. At present; I just can't imagine it.
Last edited by vich; 01-28-08 at 15:09.

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Vich,

I'll be the bearer of bad tidings. I don't think that your DB solution would work, or at least it would be impractical to implement.

For each length of raw material you would need to come up with every possible combination of cut lengths. That seems easy until your users start putting in strange, custom lengths that you've never heard of before. Then you start running into issues, like in the example that you provided, where you do not have a even number of combinations to match the possible combinations that you populated in the database.

And to add insult to injury, you will need to account for raw material stock that is longer than 6" because of the way the slats were optimized. What I mean by this is that you might have a 5' piece of raw material left that you can/could use for the next order of the same material.

I understand your situation. I work for a glass fabrication company and we cut large sheets of glass into smaller pieces for customer orders. We don't like scrap either. We purchased optimizer software instead of trying to come up with our own solution. So, no help with providing you a solution to develop something on your own.

All I can tell you is that there is a lot of complex math involved, as you guessed, and the company's that develop optimizer software spent a long time in developing and tweaking them.

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Originally Posted by HubarttMeister
...
All I can tell you is that there is a lot of complex math involved, as you guessed, and the company's that develop optimizer software spent a long time in developing and tweaking them.
Thanks for replying. It was a long shot that someone with experience in this sort of problem could convey enough to really help. Following your path (getting an optimizer) is probably some of the best advice. I wish I knew of an optimizer I could consider buying. Oh well; onward.

As fascinating as it is technically; there are just too many factors to create a solution that'll be 100%.

For example: As you imagined; we do have a warehouse section of prior left-overs (about 100 feet of 12 foot shelves, with over 200 patterns/colors - maybe 3% of our warehouse) so once they decide to use that, the whole cut-plan is bunk. Also; color-lots vary so they may need to "waste" the rest of an off-color box after using it for the bedroom blinds (or anywhere they won't hang together). The other 90% of the time; a cut-plan could pay off.

To get them started; I've decided to simply provide a new work-order section containing material quantity (linear foot) summaries. That'll at least help with their current manual addition process without interfering with a process that's been working acceptably for years.

I'll add the "Cut Plan" at a later date. It's not my primary task, so I'm just fishing for suggestions. A lot of really smart people frequent this site so I was hoping one of them has solved similar "optimizer" problems who could point the way.

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Originally Posted by vich
Following your path (getting an optimizer) is probably some of the best advice. I wish I knew of an optimizer I could consider buying. Oh well; onward.
Well, any of the optimizers I could recommend to you were designed with the glass fabrication industry in mind.

But, if I were thinking out of the box, I would say that any optimizer that would work for my industry should work in yours. I don't think that the difference between sheets of glass and blind slats are that great.

In the past my company has worked with PMC Software and their OptiMate product. There are others out there (albat-wirsam, Lisec) that are available.

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