How to cover a rectangle with least number of convex polygons cut from sheets of given size

I'm designing a big door -- a rectangle sized 3*2.6 meters. (7.8 square meters).

Given that the material I'm going with is OSB, which comes in 2.5*1.25 m. (3.125 sq.m.) sheets. Is there a tool/method to devise a cutting plan that'd use the least number of polygons to cover the rectangle?
UPD: Inspired by the answer: The smallest I've got to is with 5 rectangles cut out from 3 pieces of OSB:

• Did you have a reason for using the term "concave" in your title? I don't think that word applies to your problem. – A. I. Breveleri May 4 '17 at 15:24
• Five is the minimum number of tiles you will need. – A. I. Breveleri May 4 '17 at 15:27
• @A.I.Breveleri. Yes, of course, it's convex polygons, not concave. Can you elaborate why 5 is the minimum number of tiles? – Gleb May 4 '17 at 15:33
• I think I have a good solution to your problem but you'll need to change your question. The goal to minimize the number of polygons doesn't really make sense to me. I think what you are looking for is (1) to avoid consuming 4 sheets of OSB when 3 will do it, (2) to assemble the OSB in such a way that is structurally sound (avoid very small or narrow pieces, perhaps avoid lining up all the seams), and (3) to reduce the number of cuts you need to make, and (4) to avoid complex cuts. This is a classic tiling problem but with very large tiles and you should look to brick bonds for inspiration. – Stanwood May 4 '17 at 16:01
• I suggest dividing the 3 m length into three even 1 m lengths. Then divide the 2.6 m width into two uneven lengths. If you want to minimize cuts I suggest 1.25 m and 1.35 m. These add up to 2.5 m. Out of a single 1.25 x 2.5 board you can cut out one 1.00 x 1.25 piece and one 1.00 x 1.35 piece. It will require 3 straight cuts. Repeat three times and assemble. Change your question and I will post you a picture. – Stanwood May 4 '17 at 16:04