[Totally OT] Real Life Puzzle

Where I work, I have to take large sheets of metal off the production line
and chop it up into smaller samples that can be submitted for testing.
Whilst I have my particular method, I am sure that there's a better one out
there. Here's the scenario:

The original metal sheeting is 940mm wide by 'about' 1200mm long. The
'rolling direction' (this is important) is parallel to the 1200mm sides.

The sample sizes I need to cut out of this big sheet a

A: 165 x 120 mm
B: 165 x 120 mm
C: 165 x 120 mm
D: 270 x 95 mm
E: 270 x 95 mm
F: 270 x 95 mm
G: 230 x 95 mm
H: 300 x 125 mm
I: 300 x 125mm
J: 152 X 77 mm
K: 150 x 100 mm
L: 95 x 60 mm

AIM: The aim of the excercise is to cut all my little samples out such that
I retain the largest contiguous area that spans the width of the original
sheet, that is, the 'rolling direction' of the left over material has to be
maximised whilst the width remains at 940mm.

Rules:

* My shears can only cut in one straight line, and for safety reasons, I
have to chop any metal sheeting completley in two - I can't chop 'half way'
and then turn and chop another 'half way' to remove a corner. It probably
doesn't matter in this scenario, but all the samples have 90 degree corners,
and the shears are such that they can only make 90 degree (or 180 degree)
cuts.

* For samples A - I inclusive, the longest edge has to be parallel to the
rolling direction. Whilst it is strongly preferrable to have *all* samples
in this configuration, it is not absolutely necessary for samples J, K, & L
to be aligned this way.

* The outermost 20mm from the long edges of the original sheet has to be
excluded from all samples except H & I

Question A: How do I arrange all my samples so that I retain the longest
amount of 'full width' material?
Question B: Argh! My boss now wants me to test both sides of the material,
which means I have to take two of every sample instead of one. Is this
arrangement different to the one above (and if so, how)?

Variations for your amusement:

1) The sheet width can vary in 20 mm increments between 800 and 1200
(although 940 is the standard) at which widths does the conficuration of
samples have to change?
2) I can cheat a bit if the boss isn't looking - I don't necessarily need
the whole of Sample I if there are more two than 50mm x 50mm (or bigger)
bits (orientation not important) I can use instead.

Feel free to ask any questions, and I can send you my 'map' of how I chop
them up if you wish.

I can assure you this is a 'real' puzzle that i have to tackle many times a
year.

Yowie

"Yowie" wrote in message
...
Where I work, I have to take large sheets of metal off the
production line and chop it up into smaller samples that can be
submitted for testing. Whilst I have my particular method, I am
sure that there's a better one out there. Here's the scenario:

snip the problem

This is a problem that needs someone proficient in differential
calculus!
Alternatively, it needs a tailor's (or dress-maker's)
pattern-cutter - they do this sort of thing all the time, to
minimise loss of material.

--
MatSav

Where I work, I have to take large sheets of metal off the production
line and chop it up into smaller samples that can be submitted for
testing.

I don't think human reasoning will get the best answer to that one -
it's the sort of problem that people solve by computer optimization
techniques (simulated annealing and the like), as used by pattern
cutting software in the garment industry. Try a repost to sci.math
or sci.math.stat.

One issue you didn't raise: what if the rollers are uneven across
their width? If you cut your samples in the same way every time,
whatever test you apply to a specific piece in the cut pattern will
always hit an area that went through the same point. So you might
find that the smallest or squarest pieces were also the thinnest,
and skew the results. Multiple sample-cutting patterns, chosen to
be as different as possible, would get round that. (Look up Latin
squares and experimental designs in references on statistics to see
the issues - in this instance, you've got a very difficult problem).

==== j a c k at c a m p i n . m e . u k === http://www.campin.me.uk ====
Jack Campin, 11 Third St, Newtongrange EH22 4PU, Scotland == mob 07800 739 557
CD-ROMs and free stuff: Scottish music, food intolerance, and Mac logic fonts
****** I killfile Google posts - email me if you want to be whitelisted ******

In ,
Jack Campin - bogus address typed:
Where I work, I have to take large sheets of metal off the production
line and chop it up into smaller samples that can be submitted for
testing.

I don't think human reasoning will get the best answer to that one -
it's the sort of problem that people solve by computer optimization
techniques (simulated annealing and the like), as used by pattern
cutting software in the garment industry. Try a repost to sci.math
or sci.math.stat.

Are they friendly folks? Don't want to barge in with the impression I'm a
maths / computer geek when I am just curious about a problem that bugs me
regularly..

One issue you didn't raise: what if the rollers are uneven across
their width? If you cut your samples in the same way every time,
whatever test you apply to a specific piece in the cut pattern will
always hit an area that went through the same point. So you might
find that the smallest or squarest pieces were also the thinnest,
and skew the results. Multiple sample-cutting patterns, chosen to
be as different as possible, would get round that. (Look up Latin
squares and experimental designs in references on statistics to see
the issues - in this instance, you've got a very difficult problem).

Good call, but thankfully the steel sheet (the stuff that is turned into
metal roofing material) is extremely consistant and any defects tend to be
random rather than systematic.

Yes, I know I 'should' be randomly sampling, but its one of those things
that the practicality of not sampling randomly greatly overcomes the small
possibility of getting a systematic error by not doing so.

Yowie

Where I work, I have to take large sheets of metal off the production
line and chop it up into smaller samples that can be submitted for
testing.
I don't think human reasoning will get the best answer to that one -
it's the sort of problem that people solve by computer optimization
techniques (simulated annealing and the like), as used by pattern
cutting software in the garment industry. Try a repost to sci.math
or sci.math.stat.
Are they friendly folks? Don't want to barge in with the impression
I'm a maths / computer geek when I am just curious about a problem
that bugs me regularly..

Seems like you just want sci.math since you aren't doing a randomized
experimental design. The group is very busy and rather weird, with a
lot of utter loonies posting immense volumes of total crap. But the
way you stated your problem was precise enough to get the intelligent
life forms interested. You'll recognize a helpful answer when you see
it.

==== j a c k at c a m p i n . m e . u k === http://www.campin.me.uk ====
Jack Campin, 11 Third St, Newtongrange EH22 4PU, Scotland == mob 07800 739 557
CD-ROMs and free stuff: Scottish music, food intolerance, and Mac logic fonts
****** I killfile Google posts - email me if you want to be whitelisted ******

"Jack Campin -
Where I work, I have to take large sheets of metal off the production
line and chop it up into smaller samples that can be submitted for
testing.
I don't think human reasoning will get the best answer to that one -
it's the sort of problem that people solve by computer optimization
techniques (simulated annealing and the like), as used by pattern
cutting software in the garment industry. Try a repost to sci.math
or sci.math.stat.
Are they friendly folks? Don't want to barge in with the impression
I'm a maths / computer geek when I am just curious about a problem
that bugs me regularly..

Seems like you just want sci.math since you aren't doing a randomized
experimental design. The group is very busy and rather weird, with a
lot of utter loonies posting immense volumes of total crap. But the
way you stated your problem was precise enough to get the intelligent
life forms interested. You'll recognize a helpful answer when you see
it.

And keep lots of band-aids around I am no help at all, I'm sorry.
Good luck.
Kyla

==== j a c k at c a m p i n . m e . u k === http://www.campin.me.uk
====
Jack Campin, 11 Third St, Newtongrange EH22 4PU, Scotland == mob 07800 739
557
CD-ROMs and free stuff: Scottish music, food intolerance, and Mac logic
fonts
****** I killfile Google posts - email me if you want to be whitelisted
******

"Yowie" wrote in news:7fm8biF2lm9spU1
@mid.individual.net:

The sample sizes I need to cut out of this big sheet a

Why all the different sizes?

* My shears can only cut in one straight line, and for safety reasons,
I have to chop any metal sheeting completley in two - I can't chop
'half way' and then turn and chop another 'half way' to remove a
corner.

Are you using hand shears? This seems like a job for a big machine shear,
like the kind used to shear large reams of paper down to smaller sizes in a
printing shop.

It's too bad you don't have a laser cutter. My old job had one of those and
we did all kinds of nifty sheet metal work. At my current job we outsource
that and then have to carefully inspect the result.

In ,
ScratchMonkey typed:
"Yowie" wrote in
news:7fm8biF2lm9spU1 @mid.individual.net:

The sample sizes I need to cut out of this big sheet a

Why all the different sizes?

Coz most rests require a different size sample.


* My shears can only cut in one straight line, and for safety
reasons, I have to chop any metal sheeting completley in two - I
can't chop 'half way' and then turn and chop another 'half way' to
remove a corner.

Are you using hand shears? This seems like a job for a big machine
shear, like the kind used to shear large reams of paper down to
smaller sizes in a printing shop.

Large hydraulic shear. Hence its one cut, straight across the entire peice
of metal you are holding at a time. No dog-legs, no curves. One of hte
things I learnt early was that you couldn't do clever things by turning
samples on their sides and nesting them together as if you had a pair of
scissors.

It's too bad you don't have a laser cutter. My old job had one of
those and we did all kinds of nifty sheet metal work. At my current
job we outsource that and then have to carefully inspect the result.

Laser cutter would be lots of fun, but far to expensive for our needs. Its
one of those things, Its just me thats being conservative by trying to do
this, there's no big deal if I use up more sheeting that necessary except
for the fact that if I use it all, I can't re-sample from the left overs
later if something seems weird and I need to re-test, thats all.

Yowie

On Mon, 31 Aug 2009 14:34:54 +1000, "Yowie"
wrote:

Laser cutter would be lots of fun, but far to expensive for our needs.

Laser cutters are pretty amazing. They are cheaper than making dies
for short runs. I guess your shop only makes a _lot_ of a given part.

Bud

In ,
William Hamblen typed:
On Mon, 31 Aug 2009 14:34:54 +1000, "Yowie"
wrote:

Laser cutter would be lots of fun, but far to expensive for our
needs.

Laser cutters are pretty amazing. They are cheaper than making dies
for short runs. I guess your shop only makes a _lot_ of a given part.

We don't actually make 'parts' - we are a testing laboratory that tests
coated 9and often painted) steel sheeting, the stuff that eventually gets
roll formed and put on the roof etc.

We get a large sheet, and have to cut it down into smaller sections. I have
my particular set of test sizes, other have different sizes and
configurations they need. And sometimes we just need to trim off a
millimetre or two etc etc. The most important thing is that our sheets stay
*flat*. Hand shears tend to bend sheet metal as it cuts, and laser cutters
are great for intricate patterns but not when someone just wants to take off
'just this corner' etc etc.

Yowie