Results 1 to 3 of 3

Math Help - divide an area efficiently

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    2

    divide an area efficiently

    Hello,

    I'm not sure if this is the correct subforum but here's my question.

    I wish to create a piece of software that calculates the most efficient way of cutting certain dimensions from standard size sheets.

    I will try and explain.

    Say you have standard sheets of material measuring 2000mm x 1000mm and you need to cut an arbritary set of rectangular sizes out of such standard sheets. You may also have to use multiples of these standard sheets to get all the sizes you need. An example might be, you need 2 pieces of 100mm x 400mm, 5 sheets of 200mm x 350mm, 4 sheets of 283mm x 600mm and so forth.

    As an artist, this is something I need to do regularly and it takes me *ages* to work out the most efficient method which causes the least waste.

    If I could create software that I could simply input the sizes I need and it tells me the most efficient way, that would be a great timesaver for me.

    Unfortunately I do not know the correct mathematical formula which would help with such a problem and I wouldn't even know where to start.

    Does anybody know if this is possible?

    Regards,

    David
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by Hendragon View Post
    Hello,
    I'm not sure if this is the correct subforum but here's my question.

    I wish to create a piece of software that calculates the most efficient way of cutting certain dimensions from standard size sheets.

    I will try and explain.

    Say you have standard sheets of material measuring 2000mm x 1000mm and you need to cut an arbritary set of rectangular sizes out of such standard sheets. You may also have to use multiples of these standard sheets to get all the sizes you need. An example might be, you need 2 pieces of 100mm x 400mm, 5 sheets of 200mm x 350mm, 4 sheets of 283mm x 600mm and so forth.

    As an artist, this is something I need to do regularly and it takes me *ages* to work out the most efficient method which causes the least waste.

    If I could create software that I could simply input the sizes I need and it tells me the most efficient way, that would be a great timesaver for me.

    Unfortunately I do not know the correct mathematical formula which would help with such a problem and I wouldn't even know where to start.

    Does anybody know if this is possible?

    Regards,

    David
    There isn't a "correct mathematical formula" for placement of the tiles. There are several algorithms (do an internet search) that will assist in generating the most economical placement of the tiles.

    A similar problem is that the cost to find the least waste exceeds the value of the material wasted.

    Can one edge of a tile match the edge of another tile?
    Or is it required that a small margin remain?
    [2x4 lumber is not 2"x4"]
    You may have included that border in the tile sizing.

    My procedure:
    Similar tiles are treated as a single unit (as square as possible).
    Place the largest tile first [horizontally or vertically & then swap on the subsequent iteration]
    Then in descending size, slide & rotate the remaining pieces until all are used or an unacceptable arrangement occurs - then back track and handle the alternate.

    I really do not cut material; it is the dense packing of boxes in a container, but the idea is approximately the same.

    Best to search the web for some free code.

    .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    2
    Hello Aidan,

    Many thanks for the reply. I'll keep searching for an algorithm. With regards to the border, there is no margin that needs to remain so each edge can match the other edge of a tile.

    One other variable in this is that the cutting is done by a guillotine and therefore it cuts across the entire width of the piece I'm working with which becomes another limitation. So if I cut a sheet which is 500mm x 500mm, I'll always be left with one of the edges at 500mm which is a remainder that I then have to work with.

    A solution to this problem would be the holy grail for me!

    Thanks for your answer.

    David
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Evaluate efficiently
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 18th 2011, 12:02 AM
  2. [SOLVED] Computing efficiently
    Posted in the Math Topics Forum
    Replies: 7
    Last Post: September 4th 2010, 11:09 PM
  3. Replies: 1
    Last Post: March 9th 2010, 12:47 AM
  4. Replies: 5
    Last Post: May 27th 2009, 03:36 PM
  5. Replies: 1
    Last Post: November 29th 2007, 05:17 AM

Search Tags


/mathhelpforum @mathhelpforum