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From: Green on 22 May 2010 11:47
At my work, we cut strips of metal from 41 inch wide coil. The metal
strips vary in both length and width. Generally the length is in 2-
foot increments, ranging from 10 feet to 20 feet. The width varies
greatly. In one pass, a semi-automated metal shear first cuts the
coil metal to width (the width cut is set manually) then to length
(the length cut is programmed in).

When the shear operator gets a batch of orders, he surveys the widths
and lengths then makes a 'best-guess' at how to cut the metal strips
-- first to minimize metal consumption and second to minimize setup
time for the width cut.

If necessary, the cut strips can be moved to another shear to further
cut to length. For instance, if two strips are needed at 15 inches
wide, one 12 feet long and another 14 feet long, we cut two strips at
14 feet long. Then one of them is moved to another shear to cut from
14 feet to 12 feet.

If it can't be used immediately for another order in the batch, the
leftover metal trim is scrapped. Since the coil is 41 inches wide,
and only two 14 foot long by 15 inch wide, strips were cut, the
remaining 14 foot long by 11 inch wide strip is scrapped.

For some batches, the operator may consider dozens of 'reasonable' cut
combinations before finally settling on one 'best' solution.

I'm thinking that there is already a mathematical solution for this
problem -- one that will accept input for the coil width, all the
strips' lengths and widths, evaluate the possible cut combinations,
then display the two or three that best minimize metal consumption.

Any suggestions?

Thanks.

From: Matt on 22 May 2010 12:12
On Sat, 22 May 2010 08:47:15 -0700 (PDT), Green wrote:

>At my work, we cut strips of metal from 41 inch wide coil. The metal
>strips vary in both length and width. Generally the length is in 2-
>foot increments, ranging from 10 feet to 20 feet. The width varies
>greatly. In one pass, a semi-automated metal shear first cuts the
>coil metal to width (the width cut is set manually) then to length
>(the length cut is programmed in).
>
>When the shear operator gets a batch of orders, he surveys the widths
>and lengths then makes a 'best-guess' at how to cut the metal strips
>-- first to minimize metal consumption and second to minimize setup
>time for the width cut.
>
>If necessary, the cut strips can be moved to another shear to further
>cut to length. For instance, if two strips are needed at 15 inches
>wide, one 12 feet long and another 14 feet long, we cut two strips at
>14 feet long. Then one of them is moved to another shear to cut from
>14 feet to 12 feet.
>
>If it can't be used immediately for another order in the batch, the
>leftover metal trim is scrapped. Since the coil is 41 inches wide,
>and only two 14 foot long by 15 inch wide, strips were cut, the
>remaining 14 foot long by 11 inch wide strip is scrapped.
>
>For some batches, the operator may consider dozens of 'reasonable' cut
>combinations before finally settling on one 'best' solution.
>
>I'm thinking that there is already a mathematical solution for this
>problem -- one that will accept input for the coil width, all the
>strips' lengths and widths, evaluate the possible cut combinations,
>then display the two or three that best minimize metal consumption.
>
>Any suggestions?
>
>Thanks.

Not so much mathematical as algorithmic.
http://en.wikipedia.org/wiki/Knapsack_problem

Your version has the additional twist of machine setup time. Perhaps
the differing widths might be treated individually. You need a
computer programmer. Or maybe you're operator is really good at this
already and deserves a raise.
From: Ray Vickson on 22 May 2010 12:45
On May 22, 8:47 am, Green <GreenR...(a)yahoo.com> wrote:
> At my work, we cut strips of metal from 41 inch wide coil.  The metal
> strips vary in both length and width.  Generally the length is in 2-
> foot increments, ranging from 10 feet to 20 feet.  The width varies
> greatly.  In one pass, a semi-automated metal shear first cuts the
> coil metal to width (the width cut is set manually) then to length
> (the length cut is programmed in).
>
> When the shear operator gets a batch of orders, he surveys the widths
> and lengths then makes a 'best-guess' at how to cut the metal strips
> -- first to minimize metal consumption and second to minimize setup
> time for the width cut.
>
> If necessary, the cut strips can be moved to another shear to further
> cut to length.  For instance, if two strips are needed at 15 inches
> wide, one 12 feet long and another 14 feet long, we cut two strips at
> 14 feet long.  Then one of them is moved to another shear to cut from
> 14 feet to 12 feet.
>
> If it can't be used immediately for another order in the batch, the
> leftover metal trim is scrapped.  Since the coil is 41 inches wide,
> and only two 14 foot long by 15 inch wide, strips were cut, the
> remaining 14 foot long by 11 inch wide strip is scrapped.
>
> For some batches, the operator may consider dozens of 'reasonable' cut
> combinations before finally settling on one 'best' solution.
>
> I'm thinking that there is already a mathematical solution for this
> problem -- one that will accept input for the coil width, all the
> strips' lengths and widths, evaluate the possible cut combinations,
> then display the two or three that best minimize metal consumption.
>
> Any suggestions?
>
> Thanks.

Look up "stock-cutting problem" or "cutting-stock problem"; the Wiki
article http://en.wikipedia.org/wiki/Cutting_stock_problem isn't bad
as a starting point. Many algorithms (exact or heuristic) have been
developed for several versions of this problem, primarily by
Operations Research workers. These are used routinely in glass
cutting, paper cutting, etc. Researchers working with Blue Bell (maker
of Wrangler jeans) did a prize-winning study related to trimming
inventory by $115 million in blue-jean manufacture;
see http://www.wright.edu/~xinhui.zhang/EdelmanPrize/Slides/BlueBell%20%281985%29.pdf
..

R.G. Vickson

R.G. Vickson
From: Ray Vickson on 22 May 2010 13:46
On May 22, 8:47 am, Green <GreenR...(a)yahoo.com> wrote:
> At my work, we cut strips of metal from 41 inch wide coil.  The metal
> strips vary in both length and width.  Generally the length is in 2-
> foot increments, ranging from 10 feet to 20 feet.  The width varies
> greatly.  In one pass, a semi-automated metal shear first cuts the
> coil metal to width (the width cut is set manually) then to length
> (the length cut is programmed in).
>
> When the shear operator gets a batch of orders, he surveys the widths
> and lengths then makes a 'best-guess' at how to cut the metal strips
> -- first to minimize metal consumption and second to minimize setup
> time for the width cut.
>
> If necessary, the cut strips can be moved to another shear to further
> cut to length.  For instance, if two strips are needed at 15 inches
> wide, one 12 feet long and another 14 feet long, we cut two strips at
> 14 feet long.  Then one of them is moved to another shear to cut from
> 14 feet to 12 feet.
>
> If it can't be used immediately for another order in the batch, the
> leftover metal trim is scrapped.  Since the coil is 41 inches wide,
> and only two 14 foot long by 15 inch wide, strips were cut, the
> remaining 14 foot long by 11 inch wide strip is scrapped.
>
> For some batches, the operator may consider dozens of 'reasonable' cut
> combinations before finally settling on one 'best' solution.
>
> I'm thinking that there is already a mathematical solution for this
> problem -- one that will accept input for the coil width, all the
> strips' lengths and widths, evaluate the possible cut combinations,
> then display the two or three that best minimize metal consumption.
>
> Any suggestions?
>
> Thanks.

Look up "stock-cutting problem" or "cutting-stock problem"; the Wiki
article http://en.wikipedia.org/wiki/Cutting_stock_problem isn't bad
as a starting point. Many algorithms (exact or heuristic) have been
developed for several versions of this problem, primarily by
Operations Research workers. These are used routinely in glass
cutting, paper cutting, etc. Researchers working with Blue Bell
(maker
of Wrangler jeans) did a prize-winning study related to trimming
inventory by $115 million in blue-jean manufacture; see
http://www.wright.edu/~xinhui.zhang/EdelmanPrize/Slides/BlueBell%20%281985%29.pdf
..

R.G. Vickson
From: Chip Eastham on 23 May 2010 00:41
On May 22, 11:47 am, Green <GreenR...(a)yahoo.com> wrote:
> At my work, we cut strips of metal from 41 inch wide coil.  The metal
> strips vary in both length and width.  Generally the length is in 2-
> foot increments, ranging from 10 feet to 20 feet.  The width varies
> greatly.  In one pass, a semi-automated metal shear first cuts the
> coil metal to width (the width cut is set manually) then to length
> (the length cut is programmed in).
>
> When the shear operator gets a batch of orders, he surveys the widths
> and lengths then makes a 'best-guess' at how to cut the metal strips
> -- first to minimize metal consumption and second to minimize setup
> time for the width cut.
>
> If necessary, the cut strips can be moved to another shear to further
> cut to length.  For instance, if two strips are needed at 15 inches
> wide, one 12 feet long and another 14 feet long, we cut two strips at
> 14 feet long.  Then one of them is moved to another shear to cut from
> 14 feet to 12 feet.
>
> If it can't be used immediately for another order in the batch, the
> leftover metal trim is scrapped.  Since the coil is 41 inches wide,
> and only two 14 foot long by 15 inch wide, strips were cut, the
> remaining 14 foot long by 11 inch wide strip is scrapped.
>
> For some batches, the operator may consider dozens of 'reasonable' cut
> combinations before finally settling on one 'best' solution.
>
> I'm thinking that there is already a mathematical solution for this
> problem -- one that will accept input for the coil width, all the
> strips' lengths and widths, evaluate the possible cut combinations,
> then display the two or three that best minimize metal consumption.
>
> Any suggestions?
>
> Thanks.

Hi, Green:

At one point I put together a set of notes and
links on a slightly more general problem, where
the layout of rectangular pieces need not have
edges parallel/perpendicular to the "coil" edges:

[Q:Algorithm for optimization of sheet-metal cutting]
http://answers.google.com/answers/threadview/id/141254.html

You may find the discussion useful, but the links
to software displayed by Google Answers may also
be worth pursuing if you seek a ready made package.

regards, chip
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