Polygon plate-cutting with a given order

This note is a complement to the paper by Hoeft and Palekar which describes the problem of cutting polygonal shapes from large plates of metal or glass. More specifically, we focus on polynomial time solvability for a number of subproblems of the more general plate-cutting problem. A primary result of this note is the polynomial time solvability for the plate-cutting problem with a given order and convex polygons.