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My client sells rolls of synthetic grass to gardeners.

Roll sizes are: width $2,3,4$ meters by $25$ meter length, each.

Given any rectangular area, you may assume limit of $200$ meters,

Provide an algorithm to find the rolls set that meets the following requirements:

  1. Minimum number of cuts (slices).
  2. Minimal loss of material.

If there is more than one solution, provide all.

More assumptions:

  • Rolls must cover the whole are. It is allowed to cut larger roll to pieces. For example to cover a triangle area.
  • Price per meter is the same

If this problem rings a bell to a similar algorithm, please comment - My search failed so far. While this is a real world issue.

Thanks!

Mulli
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  • Include your attempt. Also, is $200\ m$ side of rectangle? – SarGe Aug 01 '20 at 08:16
  • @SarGe The side is up to 200 m. – Mulli Aug 01 '20 at 13:41
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    2D cutting stock problem – RobPratt Aug 01 '20 at 15:46
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    Are you after any retangular area, just those with integer meter sides? If the former, does cutting the roll lengthwise count for no more than cutting it widthwise? For a real world problem, one of those is much harder than the other. When minimum number of cuts and minimum waste work against each other (they do), which is preferable? – Paul Sinclair Aug 01 '20 at 18:15
  • @PaulSinclair Thanks for your questions.For minimal number of cuts you will often cut rolls by their length, and most likey, one on the width to get the perfect placement. My study revealed that the tradeoff bewteen loss and minimal cuts is that you can reduce loss by adding single extra cut. I shall soon add a link to what I have so far. – Mulli Aug 01 '20 at 20:43
  • @RobPratt This is not cutting stock, but usind small set of tiles (in the case above 2X25, 3X25 and 4X25) to cover area. You may need to cut tiles on the edges, but thsi is not the major issue – Mulli Aug 01 '20 at 21:11

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